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

The derivative of 1/(2sqrt(1+x)) is -1/(4(1+x)^{3/2)}

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

The first derivative of 1/(2sqrt(1+x)) is -1/(4(1+x)^{3/2)}

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

- \frac{1}{4 ( 1 + x ) ^{\frac{3}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2} (- \frac{1}{2 ( 1 + x ) ^{\frac{3}{2}}} \cdot 1) : - \frac{1}{4 ( 1 + x ) ^{\frac{3}{2}}}

= - \frac{1}{4 ( 1 + x ) ^{\frac{3}{2}}}

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

\frac{d}{d x} (cos (π \cdot x))

x^{2} \cdot e^{x} + 4 \cdot y \cdot e^{(- y)} \cdot y^{^{'}} = 0

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

\int_{0}^{x^{2}} t^{2} d t

What is the derivative of 1/(2sqrt(1+x)) ?
The derivative of 1/(2sqrt(1+x)) is -1/(4(1+x)^{3/2)}
What is the first derivative of 1/(2sqrt(1+x)) ?
The first derivative of 1/(2sqrt(1+x)) is -1/(4(1+x)^{3/2)}