What is the derivative of ((8x+5)/(8x-5))^{1/2} ?

The derivative of ((8x+5)/(8x-5))^{1/2} is -(40)/((8x+5)^{1/2)(8x-5)^{3/2}}

What is the first derivative of ((8x+5)/(8x-5))^{1/2} ?

The first derivative of ((8x+5)/(8x-5))^{1/2} is -(40)/((8x+5)^{1/2)(8x-5)^{3/2}}

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derivative of

(\frac{8 x + 5}{8 x - 5})^{\frac{1}{2}}

- \frac{40}{( 8 x + 5 ) ^{\frac{1}{2}} ( 8 x - 5 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} ((\frac{8 x + 5}{8 x - 5})^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( \frac{8 x + 5}{8 x - 5} ) ^{\frac{1}{2}}} \frac{d}{d x} (\frac{8 x + 5}{8 x - 5})

= \frac{1}{2 ( \frac{8 x + 5}{8 x - 5} ) ^{\frac{1}{2}}} \frac{d}{d x} (\frac{8 x + 5}{8 x - 5})

\frac{d}{d x} (\frac{8 x + 5}{8 x - 5}) = - \frac{80}{( 8 x - 5 ) ^{2}}

= \frac{1}{2 ( \frac{8 x + 5}{8 x - 5} ) ^{\frac{1}{2}}} (- \frac{80}{( 8 x - 5 ) ^{2}})

Simplify

\frac{1}{2 ( \frac{8 x + 5}{8 x - 5} ) ^{\frac{1}{2}}} (- \frac{80}{( 8 x - 5 ) ^{2}}) : - \frac{40}{( 8 x + 5 ) ^{\frac{1}{2}} ( 8 x - 5 ) ^{\frac{3}{2}}}

= - \frac{40}{( 8 x + 5 ) ^{\frac{1}{2}} ( 8 x - 5 ) ^{\frac{3}{2}}}

e^{r} + r^{e}

f (x) = \frac{2 x}{3 - tan ( x )}

\frac{\partial}{\partial x} (sin (8 x - 9 y))

\frac{x}{2} + 3

\frac{\partial}{\partial x} (ln (x + 2 y + 6 z))

What is the derivative of ((8x+5)/(8x-5))^{1/2} ?
The derivative of ((8x+5)/(8x-5))^{1/2} is -(40)/((8x+5)^{1/2)(8x-5)^{3/2}}
What is the first derivative of ((8x+5)/(8x-5))^{1/2} ?
The first derivative of ((8x+5)/(8x-5))^{1/2} is -(40)/((8x+5)^{1/2)(8x-5)^{3/2}}