What is the derivative of 1/(sqrt(2x+5)) ?

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

What is the first derivative of 1/(sqrt(2x+5)) ?

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

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\frac{d}{d x} (\frac{1}{2 x + 5})

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

Solution steps

\frac{d}{d x} (\frac{1}{2 x + 5})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x + 5) = 2

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

Simplify

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

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

\frac{6}{s ^{2} ( s + 2 )}

\frac{\partial}{\partial y} (x e^{x + y} - y)

\frac{d}{d x} (4 sin (\frac{x}{2}))

\int_{- \infty}^{0} \frac{1}{7 - 9 x} d x

\frac{d}{d x} (5 e^{- 2 x} + 4)

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