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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

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

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

\int_{- 2}^{3} (x - 5) d x

\int cos^{2} (3 t) d t

\frac{\partial}{\partial x} (\frac{x + y}{x ^{2} + y ^{2}})

\int (x^{2} + x - 2) d x

\frac{d}{d x} (arctan (\frac{1}{2} x))

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