What is the derivative of (24/(x^2+4x)) ?

The derivative of (24/(x^2+4x)) is -(24(2x+4))/((x^2+4x)^2)

What is the first derivative of (24/(x^2+4x)) ?

The first derivative of (24/(x^2+4x)) is -(24(2x+4))/((x^2+4x)^2)

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\frac{d}{d x} (\frac{24}{x ^{2} + 4 x})

- \frac{24 ( 2 x + 4 )}{( x ^{2} + 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{24}{x ^{2} + 4 x})

Take the constant out:

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

= 24 \frac{d}{d x} (\frac{1}{x ^{2} + 4 x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 24 \frac{d}{d x} ((x^{2} + 4 x)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} + 4 x ) ^{2}} \frac{d}{d x} (x^{2} + 4 x)

= - \frac{1}{( x ^{2} + 4 x ) ^{2}} \frac{d}{d x} (x^{2} + 4 x)

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

= 24 (- \frac{1}{( x ^{2} + 4 x ) ^{2}} (2 x + 4))

Simplify

24 (- \frac{1}{( x ^{2} + 4 x ) ^{2}} (2 x + 4)) : - \frac{24 ( 2 x + 4 )}{( x ^{2} + 4 x ) ^{2}}

= - \frac{24 ( 2 x + 4 )}{( x ^{2} + 4 x ) ^{2}}

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What is the derivative of (24/(x^2+4x)) ?
The derivative of (24/(x^2+4x)) is -(24(2x+4))/((x^2+4x)^2)
What is the first derivative of (24/(x^2+4x)) ?
The first derivative of (24/(x^2+4x)) is -(24(2x+4))/((x^2+4x)^2)