Could someone check my reasoning? thanx

Find the derivative of the function.

sin(sin[sinx])

I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the derivative of sin[sinx]. And multiply that by derivative of [sinx].

So this is what I got:

cos(sin[sinx])*cos[sinx]*cosx

Is this right?

Correct.

To find the derivative of the function sin(sin[sinx]), you correctly identified that the chain rule needs to be applied. Let's go through the steps to check your reasoning.

1. Start by differentiating the outermost function sin(sin[sinx]) with respect to x. This gives us cos(sin[sinx]).

2. Now we need to evaluate the derivative of the inner function sin[sinx]. To do this, apply the chain rule again. The derivative of sin[sinx] with respect to x is cos[sinx] multiplied by the derivative of the inside function sinx. Hence, the derivative of sin[sinx] is cos[sinx] * cosx.

3. Finally, multiply the result from step 1 (cos(sin[sinx])) by the result from step 2 (cos[sinx] * cosx) to obtain the final derivative.

Therefore, the correct derivative of sin(sin[sinx]) is cos(sin[sinx]) * cos[sinx] * cosx. Your reasoning and answer are correct!