What is the derivative of 1/((x+1)^{1/2)} ?

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{x}{x ^{- 4}}

y = - 4 x + 3

y = (3 x - 5)^{4}

\frac{d}{d r} ((r + 1)! 2^{r})

y = \frac{1}{x + 3}

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