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

The derivative of x/(1-ln(x-2)) is (2x-ln(x-2)(x-2)-2)/((x-2)(1-ln(x-2))^2)

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

The first derivative of x/(1-ln(x-2)) is (2x-ln(x-2)(x-2)-2)/((x-2)(1-ln(x-2))^2)

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derivative of

\frac{x}{1 - ln ( x - 2 )}

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

= \frac{1 \cdot ( 1 - ln ( x - 2 ) ) - ( - \frac{1}{x - 2} ) x}{( 1 - ln ( x - 2 ) ) ^{2}}

Simplify

\frac{1 \cdot ( 1 - ln ( x - 2 ) ) - ( - \frac{1}{x - 2} ) x}{( 1 - ln ( x - 2 ) ) ^{2}} : \frac{2 x - ln ( x - 2 ) ( x - 2 ) - 2}{( x - 2 ) ( 1 - ln ( x - 2 ) ) ^{2}}

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

\int e^{- 8 t} d t

\frac{d}{d x} (e^{- t} cos (π x))

y^{^{''}} - 4 y = 9 e^{t}

\int 4 sec (4 x) tan (4 x) sec^{4} (4 x) d x

e^{- 4 x^{2}}

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