What is the derivative of f(x)=x(x^2+1) ?

The derivative of f(x)=x(x^2+1) is 3x^2+1

What is the first derivative of f(x)=x(x^2+1) ?

The first derivative of f(x)=x(x^2+1) is 3x^2+1

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derivative of

f (x) = x (x^{2} + 1)

3 x^{2} + 1

Solution steps

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

\frac{d x}{d x} = 1

\frac{d}{d 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

What is the derivative of f(x)=x(x^2+1) ?
The derivative of f(x)=x(x^2+1) is 3x^2+1
What is the first derivative of f(x)=x(x^2+1) ?
The first derivative of f(x)=x(x^2+1) is 3x^2+1