What is (\partial)/(\partial x)(x(x^2+1)) ?

The answer to (\partial)/(\partial x)(x(x^2+1)) is 3x^2+1

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(\partial)/(\partial x)(x(x^2+1))

\frac{\partial}{\partial x} (x (x^{2} + 1))

3 x^{2} + 1

Solution steps

\frac{\partial}{\partial x} (x (x^{2} + 1))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + 1

= \frac{\partial}{\partial x} (x) (x^{2} + 1) + \frac{\partial}{\partial x} (x^{2} + 1) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x^{2} + 1) = 2 x

= 1 \cdot (x^{2} + 1) + 2 xx

Simplify

1 \cdot (x^{2} + 1) + 2 xx : 3 x^{2} + 1

= 3 x^{2} + 1

\frac{3}{s - 5} - \frac{2}{s + 7}

\int b^{x} d x

\frac{d y}{d x} = \frac{( x ^{2} + 1 )}{e ^{y}}

\int (\frac{x ^{2}}{1 - x ^{2}}) d x

2 t cos (t)

What is (\partial)/(\partial x)(x(x^2+1)) ?
The answer to (\partial)/(\partial x)(x(x^2+1)) is 3x^2+1