What is the derivative of-(20/((2+x)^2)) ?

The derivative of-(20/((2+x)^2)) is (40)/((2+x)^3)

What is the first derivative of-(20/((2+x)^2)) ?

The first derivative of-(20/((2+x)^2)) is (40)/((2+x)^3)

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\frac{d}{d x} (- \frac{20}{( 2 + x ) ^{2}})

\frac{40}{( 2 + x ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{20}{( 2 + x ) ^{2}})

Take the constant out:

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

= - 20 \frac{d}{d x} (\frac{1}{( 2 + x ) ^{2}})

Apply exponent rule:

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

= - 20 \frac{d}{d x} ((2 + x)^{- 2})

Apply the chain rule:

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

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

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

= - 20 (- \frac{2}{( 2 + x ) ^{3}} \cdot 1)

Simplify

- 20 (- \frac{2}{( 2 + x ) ^{3}} \cdot 1) : \frac{40}{( 2 + x ) ^{3}}

= \frac{40}{( 2 + x ) ^{3}}

e^{x} - \frac{8}{x}

x^{4} + 1

\int \frac{1}{x ^{\frac{1}{3}}} d x

\frac{d}{d x} (ln (\frac{5}{x}))

y^{^{''}} + 2 y^{^{'}} - 3 y = 2 x - 17

What is the derivative of-(20/((2+x)^2)) ?
The derivative of-(20/((2+x)^2)) is (40)/((2+x)^3)
What is the first derivative of-(20/((2+x)^2)) ?
The first derivative of-(20/((2+x)^2)) is (40)/((2+x)^3)