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

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

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

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

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derivative of

\frac{x}{1 - ln ( x - 8 )}

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

Solution steps

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

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

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

\frac{d}{d x} (1 - ln (x - 8)) = - \frac{1}{x - 8}

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

Simplify

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

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

4 x (x^{2} - 9)

x \to 0 lim (\frac{8 x}{cot ( x )})

3 x^{2} + x, at x = 1

(- 6, 4), (- 5, - 10)

f (x) = 7 x^{2}, at x = 4

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