What is the derivative of (-5)/((2x^3+7)^2) ?

The derivative of (-5)/((2x^3+7)^2) is (60x^2)/((2x^3+7)^3)

What is the first derivative of (-5)/((2x^3+7)^2) ?

The first derivative of (-5)/((2x^3+7)^2) is (60x^2)/((2x^3+7)^3)

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derivative of

\frac{- 5}{( 2 x ^{3} + 7 ) ^{2}}

\frac{60 x ^{2}}{( 2 x ^{3} + 7 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{- 5}{( 2 x ^{3} + 7 ) ^{2}})

Simplify

\frac{- 5}{( 2 x ^{3} + 7 ) ^{2}} : - \frac{5}{( 2 x ^{3} + 7 ) ^{2}}

= \frac{d}{d x} (- \frac{5}{( 2 x ^{3} + 7 ) ^{2}})

Take the constant out:

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

= - 5 \frac{d}{d x} (\frac{1}{( 2 x ^{3} + 7 ) ^{2}})

Apply exponent rule:

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

= - 5 \frac{d}{d x} ((2 x^{3} + 7)^{- 2})

Apply the chain rule:

- \frac{2}{( 2 x ^{3} + 7 ) ^{3}} \frac{d}{d x} (2 x^{3} + 7)

= - \frac{2}{( 2 x ^{3} + 7 ) ^{3}} \frac{d}{d x} (2 x^{3} + 7)

\frac{d}{d x} (2 x^{3} + 7) = 6 x^{2}

= - 5 (- \frac{2}{( 2 x ^{3} + 7 ) ^{3}} \cdot 6 x^{2})

Simplify

- 5 (- \frac{2}{( 2 x ^{3} + 7 ) ^{3}} \cdot 6 x^{2}) : \frac{60 x ^{2}}{( 2 x ^{3} + 7 ) ^{3}}

= \frac{60 x ^{2}}{( 2 x ^{3} + 7 ) ^{3}}

What is the derivative of (-5)/((2x^3+7)^2) ?
The derivative of (-5)/((2x^3+7)^2) is (60x^2)/((2x^3+7)^3)
What is the first derivative of (-5)/((2x^3+7)^2) ?
The first derivative of (-5)/((2x^3+7)^2) is (60x^2)/((2x^3+7)^3)