What is the derivative of-1/((x+3^2)) ?

The derivative of-1/((x+3^2)) is 2/((x+3)^3)

What is the first derivative of-1/((x+3^2)) ?

The first derivative of-1/((x+3^2)) is 2/((x+3)^3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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What is the derivative of-1/((x+3^2)) ?
The derivative of-1/((x+3^2)) is 2/((x+3)^3)
What is the first derivative of-1/((x+3^2)) ?
The first derivative of-1/((x+3^2)) is 2/((x+3)^3)