# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(x\cdot \left(x^2+1\right)\right)$

Learn how to solve product rule of differentiation problems step by step online.

$\frac{d}{dx}\left(x\right)\left(x^2+1\right)+x\frac{d}{dx}\left(x^2+1\right)$

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(x(x^2+1)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=x^2+1. The derivative of the linear function is equal to 1. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero.

$3x^2+1$
$\frac{d}{dx}\left(x\cdot \left(x^2+1\right)\right)$