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

Problem

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

Solution

1. Identify the outer function as cos(u) and the inner function as u=3*t

2. Apply the chain rule, which states that (d(ƒ)*(g(t)))/d(t)=ƒ′*(g(t))⋅g(t)′

3. Differentiate the outer function cos(u) with respect to u to get −sin(u)

4. Differentiate the inner function 3*t with respect to t to get 3

5. Multiply the results of the derivatives together.

6. Simplify the expression by rearranging the constants.

Final Answer

d(cos(3*t))/d(t)=−3*sin(3*t)

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