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

Problem

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

Solution

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

y=x3+x

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

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

3. Calculate the derivative of each term.

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

d(x)/d(x)=1

4. Combine the results to find the final derivative.

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

Final Answer

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

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