What is the derivative of 1/(sqrt(3-x)) ?

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

What is the first derivative of 1/(sqrt(3-x)) ?

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

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\frac{d}{d x} (\frac{1}{3 - x})

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

Solution steps

\frac{d}{d x} (\frac{1}{3 - x})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int x ln (x + 2) d x

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