What is the Chain Rule for Differentiating tan^3(x) + tan(x^3)?

[delfam]

Homework Statement

tan^3(x) + tan(x^3)

Homework Equations

The Attempt at a Solution

tan^3(x) + sec^2(x^3) + 3x^2


Im not sure how to do the tan^3(x) and not even sure I did the tan(x^3) right

 

[lanedance]

the first term is as follows
$$\frac{d}{dx} (tan(x))^3 = 3 tan^2(x)\frac{d (tan(x))}{dx} =..$$

here assume you have
$$g(x) = x^3$$
$$f(x) = tan(x)$$

and you know
$$g(x) = 3x^2$$
$$f(x) = sec(x)$$

in this form it becomes
$$g(f(x)) = (tan(x))^3 =..$$

$$\frac{d}{dx} g(f(x)) = g'(f(x))f'(x) = ...$$

finish this & try the 2nd term again as its not correct either

 

[lanedance]

expanded above