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

Problem

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

Solution

1. Identify the outer and inner functions to apply the Chain Rule. The expression is of the form un where u=sin(x) and n=3

2. Apply the Power Rule to the outer function by bringing the exponent to the front and subtracting one from the exponent.

3*sin(x)

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

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

4. Combine the results to find the final derivative.

3*sin(x)*cos(x)

Final Answer

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

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