Find the derivative of y = sin2(5x) with respect to x.
Answer Details
To find the derivative of y = sin^2(5x), we use the chain rule of differentiation, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function. In this case, the outer function is sin^2 and the inner function is 5x.
Thus,
y' = 2 sin(5x) cos(5x) * 5
Simplifying this expression, we get:
y' = 10 sin(5x) cos(5x)
Therefore, the answer is: 10 sin(5x) cos(5x).