What is the derivative of ln(((8x-9)^2)/(-x-1)) ?

The derivative of ln(((8x-9)^2)/(-x-1)) is -(8x+25)/((8x-9)(-x-1))

What is the first derivative of ln(((8x-9)^2)/(-x-1)) ?

The first derivative of ln(((8x-9)^2)/(-x-1)) is -(8x+25)/((8x-9)(-x-1))

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derivative of

ln (\frac{( 8 x - 9 ) ^{2}}{- x - 1})

- \frac{8 x + 25}{( 8 x - 9 ) ( - x - 1 )}

Solution steps

\frac{d}{d x} (ln (\frac{( 8 x - 9 ) ^{2}}{- x - 1}))

Apply the chain rule:

\frac{1}{\frac{( 8 x - 9 ) ^{2}}{- x - 1}} \frac{d}{d x} (\frac{( 8 x - 9 ) ^{2}}{- x - 1})

= \frac{1}{\frac{( 8 x - 9 ) ^{2}}{- x - 1}} \frac{d}{d x} (\frac{( 8 x - 9 ) ^{2}}{- x - 1})

\frac{d}{d x} (\frac{( 8 x - 9 ) ^{2}}{- x - 1}) = \frac{- 64 x ^{2} - 128 x + 225}{( - x - 1 ) ^{2}}

= \frac{1}{\frac{( 8 x - 9 ) ^{2}}{- x - 1}} \cdot \frac{- 64 x ^{2} - 128 x + 225}{( - x - 1 ) ^{2}}

Simplify

\frac{1}{\frac{( 8 x - 9 ) ^{2}}{- x - 1}} \cdot \frac{- 64 x ^{2} - 128 x + 225}{( - x - 1 ) ^{2}} : - \frac{8 x + 25}{( 8 x - 9 ) ( - x - 1 )}

= - \frac{8 x + 25}{( 8 x - 9 ) ( - x - 1 )}

x^{\frac{11}{2}}

x^{^{'}} = - x^{2}

f (2) = 3 x^{2} - 2 x + 5

\int \frac{x + 2}{x ^{3}} d x

\frac{\partial}{\partial x} (2 x e^{x^{2}})

What is the derivative of ln(((8x-9)^2)/(-x-1)) ?
The derivative of ln(((8x-9)^2)/(-x-1)) is -(8x+25)/((8x-9)(-x-1))
What is the first derivative of ln(((8x-9)^2)/(-x-1)) ?
The first derivative of ln(((8x-9)^2)/(-x-1)) is -(8x+25)/((8x-9)(-x-1))