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

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

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

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

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derivative of

f (x) = \frac{2 x}{x - 1}

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

= 2 \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

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

Simplify

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

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

\int sin (x) \cdot cos^{2} (x) d x

\frac{d}{d x} (e^{4 x^{2 + 1}})

x \to 0 + lim (\frac{2}{x} - \frac{3}{2})

\int cos (x) (3 + 8 sin^{2} (x)) d x

x \to 3 + lim (\frac{3 x + 2}{x - 3})

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