What is the derivative of (5x/(x-1)) ?

The derivative of (5x/(x-1)) is -5/((x-1)^2)

What is the first derivative of (5x/(x-1)) ?

The first derivative of (5x/(x-1)) is -5/((x-1)^2)

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\frac{d}{d x} (\frac{5 x}{x - 1})

- \frac{5}{( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x}{x - 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{x}{x - 1})

Apply the Quotient Rule:

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

= 5 \cdot \frac{\frac{d x}{d x} ( x - 1 ) - \frac{d}{d x} ( x - 1 ) x}{( x - 1 ) ^{2}}

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

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

= 5 \cdot \frac{1 \cdot ( x - 1 ) - 1 \cdot x}{( x - 1 ) ^{2}}

Simplify

5 \cdot \frac{1 \cdot ( x - 1 ) - 1 \cdot x}{( x - 1 ) ^{2}} : - \frac{5}{( x - 1 ) ^{2}}

= - \frac{5}{( x - 1 ) ^{2}}

\int_{1}^{6} t ln (t) d t

\frac{d}{d x} (e^{-})

\frac{d y}{d x} = x y (y - 1)

5 sin^{2} (x)

y = (6 x - 5)^{2} (3 - x^{5})^{2}

What is the derivative of (5x/(x-1)) ?
The derivative of (5x/(x-1)) is -5/((x-1)^2)
What is the first derivative of (5x/(x-1)) ?
The first derivative of (5x/(x-1)) is -5/((x-1)^2)