How do you differentiate $f(x)=csc(5x^5)$ ?

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Answer 1 · 2017-06-18T00:49:04

Use the chain rule and derivative of cosecant.

$d/dx(cscx) = -cscxcotx$ $" "$ (Memorize this)

So $d/dx(cscu) = -cscucotu (du)/dx$

$f(x) = csc(5x^5)$

$f'(x) = -csc(5x^5)cot(5x^5) d/dx(5x^5)$

$= -csc(5x^5)cot(5x^5) * (25x^4)$

$= -25x^4 csc(5x^5)cot(5x^5)$

How do you differentiate f(x)=csc(5x^5)f(x)=csc(5x^5)?