What is the derivative of 1/(sqrt(5-x)) ?

The derivative of 1/(sqrt(5-x)) is 1/(2(5-x)^{3/2)}

What is the first derivative of 1/(sqrt(5-x)) ?

The first derivative of 1/(sqrt(5-x)) is 1/(2(5-x)^{3/2)}

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\frac{d}{d x} (\frac{1}{5 - x})

\frac{1}{2 ( 5 - x ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{5 - x})

Apply exponent rule:

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

= \frac{d}{d x} ((5 - x)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 5 - x ) ^{\frac{3}{2}}} \frac{d}{d x} (5 - x)

= - \frac{1}{2 ( 5 - x ) ^{\frac{3}{2}}} \frac{d}{d x} (5 - x)

\frac{d}{d x} (5 - x) = - 1

= - \frac{1}{2 ( 5 - x ) ^{\frac{3}{2}}} (- 1)

Simplify

= \frac{1}{2 ( 5 - x ) ^{\frac{3}{2}}}

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

e^{(x - 1)^{2}}

cot (x^{8})

y = (\frac{8 x ^{2} - 5}{2 - x})^{3}

g (x) = lo g_{7} (8 x^{3} - 9 x^{2})

What is the derivative of 1/(sqrt(5-x)) ?
The derivative of 1/(sqrt(5-x)) is 1/(2(5-x)^{3/2)}
What is the first derivative of 1/(sqrt(5-x)) ?
The first derivative of 1/(sqrt(5-x)) is 1/(2(5-x)^{3/2)}