Derivatives of y=sec(x), y=cot(x), y= csc(x)

Key Questions

What is Derivatives of $y = sec (x)$ $y=sec(x)$ ?

$\frac{d}{d x} sec (x) = sec (x) tan (x)$ $d/dx sec(x)=sec(x)tan(x)$

You could memorize this, but you can work it out too by knowing some trig properties.

The trig properties we will use are:
$sec (x) = \frac{1}{cos (x)}$ $sec (x)= 1/cos(x)$
and $\frac{sin x}{cos x} = tan x$ $sin x/cos x=tan x$

Deriving:
$\frac{d}{d x} sec (x) = \frac{d}{d x} \frac{1}{cos (x)} = \frac{cos (x) (0) - 1 (- sin (x))}{cos (x) cos (x)}$ $d/dx sec (x) = d/dx 1/cos(x) = (cos (x)(0) - 1 (-sin (x)))/( cos (x)cos (x))$ (using the quotient rule)
$= \frac{sin (x)}{cos (x) cos (x)} = \frac{sin (x)}{cos (x)} \cdot (\frac{1}{cos (x)}) = tan (x) sec (x) = sec (x) tan (x)$ $= sin (x)/ (cos (x) cos (x)) = sin(x)/cos(x) *(1/cos( x)) = tan (x) sec( x)=sec (x) tan (x)$

Sally · 3 · Sep 7 2014

Questions

What is Derivatives of $y = sec (x)$ $y=sec(x)$ ?
What is the Derivative of $y = sec (x^{2})$ $y=sec(x^2)$ ?
What is the Derivative of $y = x sec (k x)$ $y=x sec(kx)$ ?
What is the Derivative of $y = {sec}^{2} (x)$ $y=sec ^ 2(x)$ ?
What is the derivative of $y = 4 {sec}^{2} (x)$ $y=4 sec ^2(x)$ ?
What is the derivative of $y = ln (sec (x) + tan (x))$ $y=ln(sec(x)+tan(x))$ ?
What is the derivative of $y = {sec}^{2} (x)$ $y=sec^2(x)$ ?
What is the derivative of $y = {sec}^{2} (x) + {tan}^{2} (x)$ $y=sec^2(x) + tan^2(x)$ ?
What is the derivative of $y = {sec}^{3} (x)$ $y=sec^3(x)$ ?
What is the derivative of $y = sec (x) tan (x)$ $y=sec(x) tan(x)$ ?
What is the derivative of $y = x sec (k x)$ $y=x sec(kx)$ ?
What is the derivative of $y = {sec}^{2} (2 x)$ $y=sec^2(2x)$ ?
What is the derivative of $y = sec (2 x) tan (2 x)$ $y=sec(2x) tan(2x)$ ?
What is the derivative of $y = {sec}^{3} (x)$ $y=sec^3(x)$ ?
What is the derivative of $y = \frac{1 - sec (x)}{tan (x)}$ $y=(1-sec(x))/tan(x)$ ?
What is the derivative of $y = e^{tan (x)}$ $y=e^(tan(x))$ ?
What is the derivative of $y = tan (arcsin (x))$ $y=tan(arcsin (x))$ ?
How do you find the derivative of $y = x^{tan (x)}$ $y=x^tan(x)$ ?
How do you find the second derivative of $y = tan (x)$ $y=tan(x)$ ?
What is the derivative of $y = tan (x) cot (x)$ $y=tan(x) cot(x)$ ?
What is the derivative of $y = tan (x) sec (x)$ $y=tan(x) sec(x)$ ?
What is the derivative of $y = \frac{tan (x)}{x}$ $y=tan(x)/x$ ?
What is the derivative of $y = tan (x^{2})$ $y=tan(x^2)$ ?
What is the derivative of $y = tan (x^{4})$ $y=tan(x^4)$ ?
How do you find the derivative of $y = tan (2 x)$ $y=tan(2x)$ ?
How do you find the derivative of $y = tan (3 x)$ $y=tan(3x)$ ?
How do you find the derivative of $y = {tan}^{2} (3 x)$ $y=tan^2(3x)$ ?
How do you find the derivative of $y = {tan}^{2} (5 x)$ $y=tan^2(5x)$ ?
What is the derivative of $y = csc (\frac{x}{2})$ $y=csc(x/2)$ ?
What is the derivative of $y = csc (x) cot (x)$ $y=csc(x) cot(x)$ ?
How do you find the derivative of $y = \frac{cos (x)}{csc (x)}$ $y=cos(x)/csc(x)$ ?
What is the derivative of $y = {csc}^{3} (x)$ $y=csc^3(x)$ ?
What is the derivative of ${csc}^{2} (x)$ $csc^2(x)$ ?
What is the derivative of ${sec}^{2} (x)$ $sec^2(x)$ ?
What is the derivative of $- csc (x)$ $-csc(x)$ ?
How do I differentiate $y = {sec}^{2} (x) + {tan}^{2} (x)$ $y= sec^2(x) + tan^2(x)$ ?
How do you find the derivative of $(sin 2 x)$ $(sin2x)$ ?
How do you differentiate $y = {sec}^{2} x + {tan}^{2} x$ $y=sec^2x+tan^2x$ ?
How do you find second derivative of $g (x) = sec (3 x + 1)$ $g(x)=sec(3x+1)$ ?
What is the second derivative of $sec x$ $secx$ ?
How do you find the derivative of $w^{2} {sec}^{2} (3 w)$ $w^2 sec^2(3w)$ ?
How do you find the derivative of $ln (csc 5 x)$ $ln(csc 5x)$ ?
How do you differentiate $y = {cos sec}^{2} (x)$ $y = cos sec^2(x)$ ?
How do you find the second derivative of ${sec}^{2} (2 x)$ $sec^2 (2x)$ ?
How do you find the derivative of $h (θ) = csc θ + e^{θ} cot θ$ $h(theta) = csctheta +e^thetacottheta$ ?
How do you evaluate the derivative of the function $f (x) = tan x cot x$ $f (x) = tan x cot x$ at the indicated point (1,1)?
How do you find $f''(x)=csc x$ ?
How do you differentiate $ln(sec^2 * x)$ ?
How do you differentiate $2cot^3x$ ?
How do you differentiate $g(t) = sqrt (t) + 4sec(t)$ ?
How do you differentiate $y = tan(x + sec x)$ ?
What is the derivative of $(12/sinx) + (1/cotx)$ ?
What is the derivative of $(cscx+cotx)^-1$ ?
How do you find the derivative of $sec^2(x)$ ?
How do you find the derivative of $(cot^(2)x)$ ?
How do you take the derivative of $y=sec^2 x + tan^2 x$ ?
How do you differentiate $f(x) = sec(x^2 + 1)^2$ ?
How do you differentiate $y=cot(1-2x^2)$ ?
How do you differentiate $f(x) = (xe)^x csc x$ ?
How do you differentiate $y= (1- sec x)/ tan x$ ?
How do you differentiate $y=(8x+sec(x))^7$ ?
How do you find the derivative of Inverse trig function $y = cos sec^2(x)$ ?
How do you find the derivative of Inverse trig function $y = (sin(3x) + cot(x^3))^8$ ?
How do you differentiate $f(x) = sec(x^2 + 1)^2$ ?
How do you differentiate $f(x) = sec(x^2 + 1)^2-tanx$ ?
How do you differentiate $f(x) = sec(x^2 + 1)-tan^2x$ ?
How do you differentiate $g(x) = (cotx + cscx)(tanx - sinx)$ ?
How do you differentiate $g(x) = (cotx + cscx)/(tanx - sinx)$ ?
How do you differentiate $g(x) = x^cosx$ ?
How do you differentiate $g(x) = 2 csc ^2x + 5 cos x$ ?
How do you differentiate $g(x) =sec^2 x + tan^2 x$ ?
How do you differentiate $g(x) =4/cosx + 1/ tanx$ ?
How do you differentiate $g(x) =cscx -x secx$ ?
How do you differentiate $g(x) =4/x-cscx$ ?
What is the derivative of $sec^2 2x$ ?
What is the derivative of $y = [(tanx - 1) / secx]$ ?
How do you find the derivative of $f(x) = xcot(x)$ ?
What is the derivative of $cot^2(sinx)$ ?
What is the derivative of $sec^-1(x^2)$ ?
What is the derivative of $sec^2 (x) - tan^2 (x)$ ?
What is the derivative of $sec^2 x - cos x$ ?
What is the derivative of $Sec^2 pi(x)$ ?
What is the derivative of $f(x) = 2 tan^(2)x-sec^(2)x$ ?
What is the derivative of $y= sec^3 x+ tan^2 x sec x$ ?
What is the antiderivative of $(sec(x)^2)(tan(x)^2)/((sec(x)^2-(R^2))$ where R is a constant?
What is the derivative of $sec^-3(x)$ ?
What is the derivative of $sec^2(x)*tan^2(x)$ ?
What is the derivative of $y=sec(3x^2)$ ?
What is the derivative of $sec(x-x^2)$ ?
What is the derivative of $sec^2(4x)$ ?
What is the derivative of $e^(sec x)$ ?
What is the derivative of $y = ( sec x + tan x )( sec x - tan x )$ ?
What is the derivative of $ln(sec^2 (x))$ ?
What is the derivative of $sec^2(3x)$ ?
What is the derivative of $sec((x^2)+3x)$ ?
What is the derivative of $f(x) = 3x sec^2 x$ ?
What is the derivative of $sec x ^5$ ?
What is the derivative of $1/(sec x - tan x)$ ?
What is the derivative of $sec(x^2-4)$ ?
What is the derivative of $sec^2 x - 1$ ?
What is the derivative of $sec^2(x^3)$ ?
How do you use the equation given $f(x)=csc(x)$ to find f '' (π/4)?
How do you find the derivative of $2secx-cscx$ ?
How do you find the derivative of $sinthetacsctheta$ ?
How do you find the derivative of $y=sec4x$ ?
How do you find the derivative of $y = tan3x – cot3x$ ?
How do you find the derivative of $y = cot5x + csc5x$ ?
How do you find the derivative of $y = csc^3(2x)$ ?
How do you find the derivative of $y = tanx + cotx$ ?
How do you find the derivative of $y = cotx(cscx)$ ?
How do you find the derivative of $y = cosx(cotx)$ ?
How do you find the derivative of $y = (2cosx)/(x+1)$ ?
How do you find the derivative of $y =sinx/(1-cosx)$ ?
How do you find the derivative of $y =(x+2)/cosx$ ?
How do you find the derivative of $y =cotx/(1-sinx)$ ?
How do you find the derivative of $y =10sinx+100$ ?
How do you find the derivative of $y=14tanxcosx+10cscx$ ?
How do you find the derivative of $x(t)=5sint+3cost$ ?
How do you find the derivative of $g(x)=sin^2x+cos^2x+secx$ ?
How do you find the derivative of $f(x)=8sinxcosx$ ?
How do you find the derivative of $y=x^5/(4sinx)$ ?
How do you find the derivative of $S(r)=9r^2+3tanr$ ?
How do you find the derivative of $q(r)=r^3cosr$ ?
How do you find the derivative of $y=10tan(20x)$ ?
How do you find the derivative of $T=4cot^3(4z)$ ?
How do you find the derivative of $y=20sin^4x$ ?
How do you find the derivative of $f(x)=3sec^7x$ ?
How do you find the derivative of $f(x)=10cos^3(4x)$ ?
How do you find the derivative of $g(x)=2csc^8(4x)$ ?
How do you find the derivative of $x(t)=4tan^4(2t)$ ?
How do you find the derivative of $y=1+tan^2(5x)$ ?
How do you find the derivative of $f(x)=sec(3x)csc(5x)$ ?
How do you find the derivative of $f(x)=csc(3x-1)$ ?
How do you find the derivative of $f(x)=pitan(pir^2-5r)$ ?
How do you find the derivative of $f(x)=(x^3-8)tan^2(5x-3)$ ?
How do you find the derivative of $f(x)=sin^2(cos^2(x))$ ?
How do you find the derivative of $f(x)=((6x-x^4)/sinx)^6$ ?
Question #3b6b1
How do you differentiate $f(x)=sec4x^5$ ?
How do you differentiate $f(x)=csc5x^5$ ?
How do you differentiate $f(x)=2secx+tanx$ ?
How do you differentiate $f(x)=(1+tan^2x)/secx$ ?
How do you differentiate $f(x)=sec(4x)/tan(4x)$ ?
How do you differentiate $f(x)=csc^4x-21cot^2x$ ?
How do you differentiate $f(x)=cot(x/2)sin(x/2)$ ?
How do you differentiate $f(x)=sec(5x)$ ?
How do you differentiate $f(x)=cot^4(3x)$ ?
How do you differentiate $f(x)=csc^3(2x)$ ?
How do you differentiate $f(x)=sec(4x)$ ?
How do you differentiate $f(x)=tan(3x)-cot(3x)$ ?
How do you differentiate $f(x)=cot(5x)+csc(5x)$ ?
How do you differentiate $f(x)=tanx+cotx$ ?
How do you differentiate $f(x)=3secx(tanx)$ ?
How do you differentiate $f(x)=cotx(cscx)$ ?
How do you differentiate $f(x)=cosx(cotx)$ ?
How do you differentiate $f(x)=(2cosx)/(x+1)$ ?
How do you differentiate $f(x)=cotx/(1-sinx)$ ?
How do you differentiate $f(x)=xsecx$ ?
How do you differentiate $f(x)=(cotx)/(1+cotx)$ ?
How do you differentiate $y=tanx-cotx$ ?
How do you differentiate $f(x)=2cscx+5cosx$ ?
How do you differentiate $g(t)=t^3cost$ ?
How do you differentiate $g(t)=4sect+tant$ ?
How do you differentiate $f(theta)=sectheta/(1+sectheta)$ ?
How do you differentiate $f(x)=(1-secx)/(tanx)$ ?
How do you differentiate $y=csctheta(theta+cottheta)$ ?
How do you differentiate $f(x)=xe^xcscx$ ?
How do you differentiate $f(x)=x^2sinxtanx$ ?
Question #70242
How do you find the derivative of $cotx$ ?
How do you find the derivative of $cscx$ ?
Question #920f7
Question #1b162
Question #0e7a0
$y=cot^4 2x$ Find $dy/dx$ ?
Differentiate $sinx/(5x+sec^2x)$ ?
If $y=1/2 sec^2x$ how we can prove that $(d^2y)/dx^2=4y(3y-1)$ ?

Differentiating Trigonometric Functions

View all chapters

Limits Involving Trigonometric Functions
Intuitive Approach to the derivative of y=sin(x)
Derivative Rules for y=cos(x) and y=tan(x)
Differentiating sin(x) from First Principles
Special Limits Involving sin(x), x, and tan(x)
Graphical Relationship Between sin(x), x, and tan(x), using Radian Measure
Derivatives of y=sec(x), y=cot(x), y= csc(x)
Differentiating Inverse Trigonometric Functions

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Derivatives of y=sec(x), y=cot(x), y= csc(x)

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Differentiating Trigonometric Functions