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

Problem

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

Solution

1. Distribute the x into the parentheses to rewrite the expression as a simple polynomial.

x*(x2+1)=x3+x

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives.

d()/d(x)*(x3+x)=d(x3)/d(x)+d(x)/d(x)

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) to each term.

d(x3)/d(x)=3*x2

d(x)/d(x)=1

4. Combine the results to find the final derivative.

3*x2+1

Final Answer

d()/d(x)*x*(x2+1)=3*x2+1

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