Find the Derivative - d/dx cos(4x^2)

Problem

d(cos(4*x2))/d(x)

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=4*x2

2. Apply the Chain Rule by differentiating the outer function with respect to the inner function and then multiplying by the derivative of the inner function.

3. Differentiate the outer function, which results in −sin(4*x2)

4. Differentiate the inner function 4*x2 using the Power Rule, which results in 8*x

5. Multiply the results together and simplify the expression.

Final Answer

d(cos(4*x2))/d(x)=−8*x*sin(4*x2)

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