What is the derivative of #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#