Find the Derivative - d/dx sin(x)^2

Problem

d(sin2(x))/d(x)

Solution

1. Identify the outer and inner functions for the chain rule, where the expression is (sin(x))2

2. Apply the power rule to the outer function, which is the square, by bringing the exponent to the front and subtracting one from the exponent.

3. Apply the chain rule by multiplying the result by the derivative of the inner function, sin(x)

4. Substitute the derivative of the inner function, which is cos(x)

5. Simplify the expression using the trigonometric identity 2*sin(x)*cos(x)=sin(2*x)

Final Answer

d(sin2(x))/d(x)=sin(2*x)

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