What is the derivative of (7x/(x-1)) ?

The derivative of (7x/(x-1)) is -7/((x-1)^2)

What is the first derivative of (7x/(x-1)) ?

The first derivative of (7x/(x-1)) is -7/((x-1)^2)

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\frac{d}{d x} (\frac{7 x}{x - 1})

- \frac{7}{( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x}{x - 1})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{x}{x - 1})

Apply the Quotient Rule:

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

= 7 \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

= 7 \cdot \frac{1 \cdot ( x - 1 ) - 1 \cdot x}{( x - 1 ) ^{2}}

Simplify

7 \cdot \frac{1 \cdot ( x - 1 ) - 1 \cdot x}{( x - 1 ) ^{2}} : - \frac{7}{( x - 1 ) ^{2}}

= - \frac{7}{( x - 1 ) ^{2}}

x \to 0 lim (x^{x})

\int sec^{2} (\frac{x}{3}) d x

\frac{\partial}{\partial x} (ln (4 x))

y = 5 x^{2} - 10 x - 6 x^{- 2}

\frac{d}{d x} (\frac{sin ( x )}{cos ( x )})

What is the derivative of (7x/(x-1)) ?
The derivative of (7x/(x-1)) is -7/((x-1)^2)
What is the first derivative of (7x/(x-1)) ?
The first derivative of (7x/(x-1)) is -7/((x-1)^2)