Find the Derivative - d/dt cos((pit)/4)

Problem

d()/d(t)*cos((π*t)/4)

Solution

1. Identify the outer function as cos(u) and the inner function as u=(π*t)/4

2. Apply the chain rule, which states that d()/d(t)*ƒ*(g(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 (π*t)/4 with respect to t to get π/4

5. Multiply the results of the derivatives together.

6. Simplify the expression by placing the constant coefficient at the front.

Final Answer

d(cos((π*t)/4))/d(t)=−π/4*sin((π*t)/4)

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