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

Problem

d(x2+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 u2 with respect to u where u=x2+1

3. Differentiate the inner function x2+1 with respect to x

4. Multiply the results together.

d(x2+1)/d(x)=2*(x2+1)⋅d(x2+1)/d(x)

5. Calculate the derivative of the inner part.

d(x2+1)/d(x)=2*x

6. Simplify the final expression by multiplying the terms.

2*(x2+1)⋅2*x=4*x*(x2+1)

Final Answer

d(x2+1)/d(x)=4*x*(x2+1)

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