Why Is the Derivative of sin(ax²) Equal to 2axcos(ax²)?

[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.

 

[MarneMath]

Do you know the chain rule?

 

[DonAntonio]

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.

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

 

[wahaj]

that makes a lot more sense. thanks