Calculating the First Derivative

[bill nye scienceguy!]

what is the first derivative?

 

[VietDao29]

what is the first derivative?

So what do you think? What have you tried? (Have you tried anything?) And where do you get stuck?
I'll give you a hint: You should use the chain rule to solve this problem:
$$\frac{df}{dx} = \frac{df}{du} \times \frac{du}{dx}$$
Now, you have y = a sinⁿx, if you let u = sin x, you'll have:
y = auⁿ. And the chain rule states that y'_x = y'_u u'_x. Can you go from here? :)

 

[arildno]

Set u(x)=sin(x) and use the chain rule of differentiation.