What is the derivative of $f (x) = {(1 - {cos}^{2} (5 x))}^{3}$ $f(x)=(1-cos^2(5x))^3$ ?

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Answer 1 · 2018-01-15T08:53:10

$f'(x)=30cos(5x)sin(5x)^5$

$f(x)=(1-cos^2(5x))^3$

Using the identity $sin^x+cos^2x-=1$ we can get:

$f(x)=(sin^2(5x))^3=(sin(5x)^2)^3=sin^6(5x)$

$f'(x)=d/(dx)[sin(5x)^6]$

$color(white)(XXll)=d/(dx)[sin(5x)]*6sin(5x)^(6-1)$

$u=5x$

$color(white)(XXll)=(d/(dx)[sinu]*d/(dx)[5x])*6sin(5x)^5$

$color(white)(XXll)=(cosu*5)*6sin(5x)^5$

$color(white)(XXll)=(5cos(5x))*6sin(5x)^5$

$color(white)(XXll)=30cos(5x)sin(5x)^5$

What is the derivative of f(x)=(1-cos^2(5x))^3f(x)=(1−cos2(5x))3f(x)=(1-cos^2(5x))^3 ?