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,

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

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