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Popular Calculus >

derivative of 1/(sqrt(1+x))

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Simplify

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

Graph

Popular Examples

derivative of e^{1/2}

\frac{d}{d x} (e^{\frac{1}{2}})

integral of (1-x)/(x^3)

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

(dy)/(dx)=(x-18)^2

\frac{d y}{d x} = (x - 18)^{2}

limit as x approaches 4 of 9/x

x \to 4 lim (\frac{9}{x})

inverse oflaplace (2s)/((s^2+25)(s-1))

in v erse l a pl a ce \frac{2 s}{( s ^{2} + 25 ) ( s - 1 )}

Frequently Asked Questions (FAQ)

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