How do you differentiate # f(x) = tan^2(3x) #?

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Answer 1 · 2018-03-26T12:19:36

#If " f(x) = "tan^2(3x)#, then

#color(blue)((d)/(dx) f(x) = f'(x)=6 sec^2 (3x) * tan (3x)#

Given:

#f(x) = "tan^2(3x)#

We can write this function as

#f(x) = "tan(3x)^2#

#d/(dx) tan(3x)^2#

#rArr 2 tan (3x) (d/dx) tan (3x)#

#rArr 2 *tan (3x) *Sec^2 (3x)*3#

#rArr 6*sec^2(3x)*tan(3x)#

Hence,

#color(blue)((d)/(dx) f(x) = f'(x)= "6 sec^2 (3x) * tan (3x)#