What is the derivative of 4/((x^2+9^3)) ?

The derivative of 4/((x^2+9^3)) is -(24x)/((x^2+9)^4)

What is the first derivative of 4/((x^2+9^3)) ?

The first derivative of 4/((x^2+9^3)) is -(24x)/((x^2+9)^4)

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\frac{d}{d x} (\frac{4}{( x ^{2} + 9 ) ^{3}})

- \frac{24 x}{( x ^{2} + 9 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{4}{( x ^{2} + 9 ) ^{3}})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{( x ^{2} + 9 ) ^{3}})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((x^{2} + 9)^{- 3})

Apply the chain rule:

- \frac{3}{( x ^{2} + 9 ) ^{4}} \frac{d}{d x} (x^{2} + 9)

= - \frac{3}{( x ^{2} + 9 ) ^{4}} \frac{d}{d x} (x^{2} + 9)

\frac{d}{d x} (x^{2} + 9) = 2 x

= 4 (- \frac{3}{( x ^{2} + 9 ) ^{4}} \cdot 2 x)

Simplify

4 (- \frac{3}{( x ^{2} + 9 ) ^{4}} \cdot 2 x) : - \frac{24 x}{( x ^{2} + 9 ) ^{4}}

= - \frac{24 x}{( x ^{2} + 9 ) ^{4}}

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What is the derivative of 4/((x^2+9^3)) ?
The derivative of 4/((x^2+9^3)) is -(24x)/((x^2+9)^4)
What is the first derivative of 4/((x^2+9^3)) ?
The first derivative of 4/((x^2+9^3)) is -(24x)/((x^2+9)^4)