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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int sec (a x) d x

\frac{d}{d x} ((4 x^{2} - 14)^{- 10})

\int \frac{1}{( x ^{2} - 6 x + 25 ) ^{3}} d x

\int_{1}^{2} \frac{- 8 ln ( x )}{x ^{2}} d x

(x - 1)^{3}

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