# Explanation for this derivative

1. Oct 20, 2012

### wahaj

The derivative of sin(ax²) is 2axcos(ax²). Why is that? I understand the cos(ax²) part of the derivative but I don't understand where the 2ax is coming from.

2. Oct 20, 2012

### MarneMath

Do you know the chain rule?

3. Oct 20, 2012

### DonAntonio

You can google "Chain rule". It says that

$$\left(f(g(x)\right)'=f'(g(x))\cdot g'(x)$$

In the present case we have $\,f(x)=\sin x\,\,\,,\,\,\,g(x)=ax^2\,$

DonAntonio

4. Oct 20, 2012

### wahaj

that makes a lot more sense. thanks