Find the Derivative - d/dx cos(theta^2)

Problem

d(cos(θ2))/d(θ)

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=θ2

2. Apply the Chain Rule by taking the derivative of the outer function with respect to the inner function, then multiplying by the derivative of the inner function with respect to θ

3. Differentiate the outer function cos(u) which results in −sin(u)

4. Differentiate the inner function θ2 using the Power Rule, which results in 2*θ

5. Combine the results and substitute u=θ2 back into the expression.

Final Answer

d(cos(θ2))/d(θ)=−2*θ*sin(θ2)

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