What is the derivative of (20/(x+1)) ?

The derivative of (20/(x+1)) is -(20)/((x+1)^2)

What is the first derivative of (20/(x+1)) ?

The first derivative of (20/(x+1)) is -(20)/((x+1)^2)

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\frac{d}{d x} (\frac{20}{x + 1})

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

Solution steps

\frac{d}{d x} (\frac{20}{x + 1})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to + 0 lim (\frac{7}{x} - \frac{7}{x ^{2} - x})

x \to 0 lim (2 - \frac{1}{x ^{3}})

x \to 0 lim (2 - x)

x \to 5 lim (2 x + 1)

\frac{\partial}{\partial y} (x y - \frac{2}{x} - \frac{4}{y} + 8)

What is the derivative of (20/(x+1)) ?
The derivative of (20/(x+1)) is -(20)/((x+1)^2)
What is the first derivative of (20/(x+1)) ?
The first derivative of (20/(x+1)) is -(20)/((x+1)^2)