Find the Derivative - d/dx y=sin(x)^3

Problem

d()/d(x)*sin(x)

Solution

1. Identify the function as a power of a trigonometric function, which can be written as (sin(x))3

2. Apply the power rule by bringing the exponent 3 to the front and decreasing the power by 1

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

4. Differentiate the inner function, where d(sin(x))/d(x)=cos(x)

5. Simplify the expression by combining the terms.

Final Answer

d(sin(x))/d(x)=3*sin(x)*cos(x)

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