What is the derivative of (24)/(x^2+12) ?

The derivative of (24)/(x^2+12) is -(48x)/((x^2+12)^2)

What is the first derivative of (24)/(x^2+12) ?

The first derivative of (24)/(x^2+12) is -(48x)/((x^2+12)^2)

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derivative of

\frac{24}{x ^{2} + 12}

- \frac{48 x}{( x ^{2} + 12 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{24}{x ^{2} + 12})

Take the constant out:

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

= 24 \frac{d}{d x} (\frac{1}{x ^{2} + 12})

Apply exponent rule:

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

= 24 \frac{d}{d x} ((x^{2} + 12)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} + 12 ) ^{2}} \frac{d}{d x} (x^{2} + 12)

= - \frac{1}{( x ^{2} + 12 ) ^{2}} \frac{d}{d x} (x^{2} + 12)

\frac{d}{d x} (x^{2} + 12) = 2 x

= 24 (- \frac{1}{( x ^{2} + 12 ) ^{2}} \cdot 2 x)

Simplify

24 (- \frac{1}{( x ^{2} + 12 ) ^{2}} \cdot 2 x) : - \frac{48 x}{( x ^{2} + 12 ) ^{2}}

= - \frac{48 x}{( x ^{2} + 12 ) ^{2}}

x 3600 - x^{2}

3 e^{- 2 t} + e^{- t}

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What is the derivative of (24)/(x^2+12) ?
The derivative of (24)/(x^2+12) is -(48x)/((x^2+12)^2)
What is the first derivative of (24)/(x^2+12) ?
The first derivative of (24)/(x^2+12) is -(48x)/((x^2+12)^2)