Find the Derivative - d/dx (x^2+1)^2

Problem

d(x^2+1)/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule.

2. Apply the Chain Rule by taking the derivative of the outer function u^2 with respect to u where u=x^2+1

3. Differentiate the inner function x^2+1 with respect to x

4. Multiply the results together.

d(x^2+1)/d(x)=2*(x^2+1)⋅d(x^2+1)/d(x)

5. Calculate the derivative of the inner part.

d(x^2+1)/d(x)=2*x

6. Simplify the final expression by multiplying the terms.

2*(x^2+1)⋅2*x=4*x*(x^2+1)

Final Answer

d(x^2+1)/d(x)=4*x*(x^2+1)

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