Find the Derivative - d/dx sin(x)^5

Problem

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

Solution

1. Identify the outer and inner functions to apply the Power Rule and the Chain Rule. The expression is of the form un where u=sin(x) and n=5

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

d(sin(x))/d(x)=5*sin(x)⋅d(sin(x))/d(x)

3. Differentiate the inner function sin(x) with respect to x

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

4. Multiply the results together to find the final derivative.

5*sin(x)⋅cos(x)

Final Answer

d(sin(x))/d(x)=5*sin(x)*cos(x)

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