Find the Derivative - d/d@VAR f(theta)=cos(theta^2)

Problem

d()/d(θ)*cos(θ2)

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. Differentiate the outer function with respect to the inner function. The derivative of cos(u) is −sin(u)

3. Differentiate the inner function with respect to θ The derivative of θ2 is 2*θ

4. Multiply the results of the derivatives together according to the Chain Rule formula d(ƒ)/d(θ)=d(ƒ)/d(u)⋅d(u)/d(θ)

5. Simplify the resulting expression by rearranging the terms.

Final Answer

d(cos(θ2))/d(θ)=−2*θ*sin(θ2)

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