What is the derivative of x/(1-ln(x-3)) ?

The derivative of x/(1-ln(x-3)) is (2x-ln(x-3)(x-3)-3)/((x-3)(1-ln(x-3))^2)

What is the first derivative of x/(1-ln(x-3)) ?

The first derivative of x/(1-ln(x-3)) is (2x-ln(x-3)(x-3)-3)/((x-3)(1-ln(x-3))^2)

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\frac{d}{d x} (\frac{x}{1 - ln ( x - 3 )})

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

Solution steps

\frac{d}{d x} (\frac{x}{1 - ln ( x - 3 )})

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

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

\frac{d}{d x} (1 - ln (x - 3)) = - \frac{1}{x - 3}

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

Simplify

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

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

x \to 0 lim (\frac{4 ^{x} - 2 ^{x}}{x})

\frac{d}{d x} (a - b x^{2})

\int_{1}^{2} (2 x - 3)^{2} d x

y^{^{'}} + 7 y = t + e^{- 4 t}

\frac{d}{d x} (4 (3 - 9 x)^{3})

What is the derivative of x/(1-ln(x-3)) ?
The derivative of x/(1-ln(x-3)) is (2x-ln(x-3)(x-3)-3)/((x-3)(1-ln(x-3))^2)
What is the first derivative of x/(1-ln(x-3)) ?
The first derivative of x/(1-ln(x-3)) is (2x-ln(x-3)(x-3)-3)/((x-3)(1-ln(x-3))^2)