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

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

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

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

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derivative of

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

2

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (2) = 0

= 2 (1 + 0)

Simplify

= 2

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