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

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

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

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

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derivative of

\frac{- 1}{( x + 1 )}

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

Solution steps

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

Simplify

\frac{- 1}{x + 1} : - \frac{1}{x + 1}

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

Take the constant out:

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

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

Apply exponent rule:

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

= - \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

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

Simplify

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

\frac{2}{x ^{- 5}}

e^{0.5} t

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

x^{4} - x - 10

x^{4} (x^{8} + 2)

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