How do I find the derivative of sin^2(x) or written as sin(x)^2?

sin^2(x) and [sin(x)]^2 mean the same thing. They are not the same as sin(x^2).

The derivative of sin^2(x) is
2 sinx cosx = sin(2x)

Think of u(x) as sin x and use the chain rule df/dx = df/du * du/dx = 2u *sinx

I was confusing it with sin(x^2). Thank you for clearing this up for me! I have to pay attention to those parenthesis on my exam!

To find the derivative of sin^2(x) or sin(x)^2, we can apply the chain rule.

The chain rule states that for a composition of functions, the derivative of the outer function multiplied by the derivative of the inner function will give us the derivative of the whole composition.

Let's break down sin^2(x) as a composition of functions:
- The outer function is f(x) = x^2
- The inner function is g(x) = sin(x)

Now, let's find the derivatives of each function separately:
- The derivative of the outer function f(x) = x^2 is f'(x) = 2x.
- The derivative of the inner function g(x) = sin(x) is g'(x) = cos(x).

To find the derivative of sin^2(x) or sin(x)^2, we apply the chain rule:
- The derivative of sin^2(x) is (f(g(x)))' = f'(g(x)) * g'(x), where f'(g(x)) represents the derivative of the outer function evaluated at the inner function.

Substituting the derivatives we found earlier, we have:
- The derivative of sin^2(x) is 2 * sin(x) * cos(x).
- The derivative of sin(x)^2 is 2 * sin(x) * cos(x).

So, the derivative of sin^2(x) or sin(x)^2 is 2 * sin(x) * cos(x).