Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you use the limit definition to find the derivative of $y = cscx$ ?

1 Answer

Dec 2, 2016

The key parts are in the explanation section, below.

Explanation:

$(1/sin(x+h)-1/sinx)/h = (sinx-sin(x+h))/(hsin(x+h)sinx)$

$= (sinx-sinxcos h-cosxsin h)/(hsin(x+h)sinx)$

$= (sinx(1-cos h)/h - cosxsin h/h)*1/(sin(x+h)sinx)$

Taking the limit gets us

$(-cosx)/sin^2 x = -cscxcotx$

Related questions

What is the limit definition of the derivative of the function $y=f(x)$ ?
Ho do I use the limit definition of derivative to find $f'(x)$ for $f(x)=3x^2+x$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=sqrt(x+3)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=1/(1-x)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=x^3-2$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=1/sqrt(x)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=5x-9x^2$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=sqrt(2+6x)$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=mx+b$ ?
How do I use the limit definition of derivative to find $f'(x)$ for $f(x)=c$ ?

See all questions in Limit Definition of Derivative

Impact of this question

7367 views around the world

You can reuse this answer
Creative Commons License