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Popular >

derivative of ln((8x/(x+5)))

Solution

\frac{d}{d x} (ln (\frac{8 x}{x + 5}))

Solution

\frac{5}{x ( x + 5 )}

Solution steps

\frac{d}{d x} (ln (\frac{8 x}{x + 5}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{8 x}{x + 5}) = \frac{40}{( x + 5 ) ^{2}}

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

Simplify

\frac{1}{\frac{8 x}{x + 5}} \cdot \frac{40}{( x + 5 ) ^{2}} : \frac{5}{x ( x + 5 )}

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

Popular Examples

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\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{8}})

derivative of (x+y/(xy))

\frac{d}{d x} (\frac{x + y}{x y})

y^{^{'}} = 1 - \frac{y}{20}

7x^2y^'=y^'+9xe-y

7 x^{2} y^{^{'}} = y^{^{'}} + 9 x e - y

Frequently Asked Questions (FAQ)

What is the derivative of ln((8x/(x+5))) ?
The derivative of ln((8x/(x+5))) is 5/(x(x+5))
What is the first derivative of ln((8x/(x+5))) ?
The first derivative of ln((8x/(x+5))) is 5/(x(x+5))