Question

How do you find the derivative for `k(x) = sin (x^2+2)`?

Answer 1

Using the chain rule, which states that the derivative of `f(g(x))` is `f'(g(x)) * g'(x)`. In your case, the outer function `f(x)` is `\sin(x)`, and the inner function `g(x)` is `x^2+2`.

This means that `f'(x)=\cos(x)`, and `g'(x)=2x`.

Plugging these results into the chain rule formula, we get

`d/dx sin(x^2+2)= \cos(x^2+2) * 2x`