Final Answer
$3x^2+1$
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Step-by-step Solution
Problem to solve:
$\frac{d}{dx}\left(x\cdot\left(x^2+1\right)\right)$
Specify the solving method
1
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=x^2+1$
$\frac{d}{dx}\left(x\right)\left(x^2+1\right)+x\frac{d}{dx}\left(x^2+1\right)$
Learn how to solve differential calculus 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 differential calculus problems step by step online. Find the derivative of 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 or more functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero.
Final Answer
$3x^2+1$