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

The derivative of f(x)=(2x+1)/(x-1) is -3/((x-1)^2)

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

The first derivative of f(x)=(2x+1)/(x-1) is -3/((x-1)^2)

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{\frac{d}{d x} ( ln ( x ) )}{x})

x^{2}, 8 + x

f (x) = - 3 e^{- 5 x}

\frac{d}{d x} (\frac{x + 4}{x - 3})

cos^{9} (x)

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