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

Problem

d(cos(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=x2

2. Apply the Chain Rule which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

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

4. Differentiate the inner function x2 with respect to x which results in 2*x

5. Multiply the results together and substitute x2 back in for u

Final Answer

d(cos(x2))/d(x)=−2*x*sin(x2)

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