What is the derivative of x(x^2+4) ?

The derivative of x(x^2+4) is 3x^2+4

What is the first derivative of x(x^2+4) ?

The first derivative of x(x^2+4) is 3x^2+4

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derivative of

x (x^{2} + 4)

3 x^{2} + 4

Solution steps

\frac{d}{d x} (x (x^{2} + 4))

Apply the Product Rule:

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

f = x, g = x^{2} + 4

= \frac{d x}{d x} (x^{2} + 4) + \frac{d}{d x} (x^{2} + 4) x

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

\frac{d}{d x} (x^{2} + 4) = 2 x

= 1 \cdot (x^{2} + 4) + 2 xx

Simplify

1 \cdot (x^{2} + 4) + 2 xx : 3 x^{2} + 4

= 3 x^{2} + 4

What is the derivative of x(x^2+4) ?
The derivative of x(x^2+4) is 3x^2+4
What is the first derivative of x(x^2+4) ?
The first derivative of x(x^2+4) is 3x^2+4