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Popular >

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

Solution

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

Solution

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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