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

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

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

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

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derivative of

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

2 (3 x^{2} + 1)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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

= 2 (\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

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

Simplify

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

= 2 (3 x^{2} + 1)

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