How do you differentiate sine x squared?

Answer 1

Using the Chain Rule :

derivative of (sinx)2 = 2(sinx)1 * (derivative of sinx)

d/dx (Sinx)2 = 2(sinx)1 * [d/dx (Sinx)]

d/dx (Sinx)2 = 2(sinx) * (cosx)

d/dx (Sinx)2 = 2 (sinx) * (cosx)

d/dx (Sinx)2 = 2 sin(x) * cos(x)

Answer 2

Do you mean sin(x2) or sin(x)2?

In each case, you would apply the chain rule. The derivative of the sine function is the cosine, and the derivative with respect to x of axn is nax(n - 1).

So if you mean:

f(x) = sin(x2)

Then:

f'(x) = cos(x2) * 2x

If you mean:

f(x) = sin(x)2

Then:

f'(x) = 2sin(x) * cos(x)