What is the derivative of $tan^3(x) + tan(x^3)$ ?

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Answer 1 · 2017-02-26T19:06:06

$3tan^2 x sec^2 x + 3x^2 sec^2x^3$

Power rule: $(n^n)' = n u^(n-1) u'$
$(tan u)' = u' sec^2 u$

Let $n = 3$

Rewrite original equation: $f(x) = (tan x)^3 + tan(x^3)$

Use the chain rule:
$f(x)' = 3(tan x)^2 (sec^2 x) + sec^2 (x^3) (3x^2)$

Rearrange: $f(x)' = 3tan^2 x sec^2 x + 3x^2 sec^2x^3$

What is the derivative of tan^3(x) + tan(x^3) tan^3(x) + tan(x^3) ?