What is derivative of $\sin ax$ where $a$ is a constant?

Question

What is the derivative of $\sin a x$ where $a$ is a constant.

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Actually, I'm studying Physics and not so well-versed with calculus. So, I have studied the basic rules of calculus but am stuck here.

I somewhat know about the product rule but don't get what to do if a constant is given in a trigonometric function, be it $\sin ax $ or $\cos ax$. Whatever.. Please help me get my concept clear.

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Thank You!

Answer 1

HINT

Recall that by chain rule

$$\frac{d}{dx}[\sin (f(x))]=\cos (f(x))\cdot f'(x)$$

Answer 2

Derivative of $\sin(ax) = a \cos(ax)$ by Chain Rule.

Answer 3

\begin{array}{c} \frac{d}{{dx}}\left( {\sin ax} \right) = \left( {\cos ax} \right)\frac{d}{{dx}}\left( {ax} \right)\\ = \left( {\cos ax} \right) \cdot a \cdot \frac{{dx}}{{dx}}\\ = \left( {\cos ax} \right) \cdot a \cdot 1\\ = a\left( {\cos ax} \right) \end{array}