Find the Derivative - d/dt cos(2t)

Problem

d(cos(2*t))/d(t)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is cos(u) and the inner function is u=2*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 which results in −sin(u)

4. Differentiate the inner function 2*t with respect to t which results in 2

5. Multiply the results together and substitute u=2*t back into the expression.

6. Simplify the final expression by placing the constant coefficient in front.

Final Answer

d(cos(2*t))/d(t)=−2*sin(2*t)

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