# Chain Rule Again, Sorry

1. Aug 1, 2010

### delfam

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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

2. Aug 1, 2010

### 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

3. Aug 1, 2010

### lanedance

expanded above