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

The derivative of f(x)=(5x+1)/(x-1) is -6/((x-1)^2)

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

The first derivative of f(x)=(5x+1)/(x-1) is -6/((x-1)^2)

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derivative of

f (x) = \frac{5 x + 1}{x - 1}

- \frac{6}{( x - 1 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{5 ( x - 1 ) - 1 \cdot ( 5 x + 1 )}{( x - 1 ) ^{2}} : - \frac{6}{( x - 1 ) ^{2}}

= - \frac{6}{( x - 1 ) ^{2}}

y = x^{2} - 4, y = 8 - 2 x^{2}

\frac{\partial}{\partial y} (- 3 e^{x} cos (yz))

\int \frac{2 x}{x ^{2} - 7 x + 12} d x

\frac{d y}{d x} = \frac{2 + y}{x + 1}

f (x) = 5 x^{2} - x^{3}, (1, 4)

What is the derivative of f(x)=(5x+1)/(x-1) ?
The derivative of f(x)=(5x+1)/(x-1) is -6/((x-1)^2)
What is the first derivative of f(x)=(5x+1)/(x-1) ?
The first derivative of f(x)=(5x+1)/(x-1) is -6/((x-1)^2)