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

Problem

d(sin(x2))/d(x)

Solution

1. Identify the outer function as sin(u) and the inner function as 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 sin(u) with respect to u to get cos(u)

4. Differentiate the inner function x2 with respect to x to get 2*x

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

Final Answer

d(sin(x2))/d(x)=2*x*cos(x2)

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