# Math Help - Calclus I Help

1. ## Calclus I Help

1. Write the precise definition for a function f(x) defined for all values of x to be a differentiable function.

2. Can someone explain to me how the dervative of sin(x^2) is 2x cos (x^2)?

2. Originally Posted by Nimmy
2. Can someone explain to me how the dervative of sin(x^2) is 2x cos (x^2)?
Use the chain rule. Let $f(x) = sin(x)$ and $g(x) = x^2$

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

$\frac{d}{dx}(sin(x^2)) = cos(x^2) \cdot 2x$

-Dan