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

Problem

d(cos(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=cos(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*cos(x)

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

3*cos(x)⋅d(cos(x))/d(x)

4. Differentiate the inner function cos(x) which results in −sin(x)

3*cos(x)⋅(−sin(x))

5. Simplify the expression by moving the negative sign to the front.

−3*cos(x)*sin(x)

Final Answer

d(cos(x))/d(x)=−3*cos(x)*sin(x)

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