What is the derivative of x(x^2-5) ?

The derivative of x(x^2-5) is 3x^2-5

What is the first derivative of x(x^2-5) ?

The first derivative of x(x^2-5) is 3x^2-5

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\frac{d}{d x} (x (x^{2} - 5))

3 x^{2} - 5

Solution steps

\frac{d}{d x} (x (x^{2} - 5))

Apply the Product Rule:

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

f = x, g = x^{2} - 5

= \frac{d x}{d x} (x^{2} - 5) + \frac{d}{d x} (x^{2} - 5) x

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

\frac{d}{d x} (x^{2} - 5) = 2 x

= 1 \cdot (x^{2} - 5) + 2 xx

Simplify

1 \cdot (x^{2} - 5) + 2 xx : 3 x^{2} - 5

= 3 x^{2} - 5

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What is the derivative of x(x^2-5) ?
The derivative of x(x^2-5) is 3x^2-5
What is the first derivative of x(x^2-5) ?
The first derivative of x(x^2-5) is 3x^2-5