Find the Derivative - d/dt cos(t)^3

Problem

d(cos(t))/d(t)

Solution

1. Identify the outer and inner functions to apply the Power Rule and the Chain Rule. The expression is of the form u3 where u=cos(t)

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

d(cos(t))/d(t)=3*cos(t)⋅d(cos(t))/d(t)

3. Differentiate the inner function cos(t) with respect to t which results in −sin(t)

d(cos(t))/d(t)=−sin(t)

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

3*cos(t)⋅(−sin(t))=−3*cos(t)*sin(t)

Final Answer

d(cos(t))/d(t)=−3*cos(t)*sin(t)

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