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

The derivative of-2/((2x+3^2)) is 8/((2x+3)^3)

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

The first derivative of-2/((2x+3^2)) is 8/((2x+3)^3)

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

\frac{8}{( 2 x + 3 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

- 2 (- \frac{2}{( 2 x + 3 ) ^{3}} \cdot 2) : \frac{8}{( 2 x + 3 ) ^{3}}

= \frac{8}{( 2 x + 3 ) ^{3}}

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What is the derivative of-2/((2x+3^2)) ?
The derivative of-2/((2x+3^2)) is 8/((2x+3)^3)
What is the first derivative of-2/((2x+3^2)) ?
The first derivative of-2/((2x+3^2)) is 8/((2x+3)^3)