How do you find the derivative of $sec x tan x$ $secx tanx$ ?

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How do you find the derivative of $sec x tan x$ $secx tanx$ ?

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Answer 1 · 2015-08-31T16:56:09

Use the product rule and derivatives of trigonometric functions.

Explanation:

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

$= (sec x tan x) tan x + sec x ({sec}^{2} x)$ $= (secxtanx)tanx+secx(sec^2x)$

$= {sec tan}^{2} x + {sec}^{3} x$ $= sec tan^2x + sec^3x$

$= sec x ({tan}^{2} x + {sec}^{2} x)$ $= secx(tan^2x+sec^2x)$

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How do you find the derivative of $sec x tan x$ $secx tanx$ ?

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