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Popular Calculus >

derivative of f(x)=(2x+5)/(x-1)

Solution

derivative of

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

Solution

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

Solution steps

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

\frac{d}{d x} (2 x + 5) = 2

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

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

Simplify

\frac{2 ( x - 1 ) - 1 \cdot ( 2 x + 5 )}{( x - 1 ) ^{2}} : - \frac{7}{( x - 1 ) ^{2}}

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

Graph

Popular Examples

integral of 1/(x^4sqrt(16x^2-9))

\int \frac{1}{x ^{4} 16 x ^{2} - 9} d x

integral of (5x^2+3x+5)/((x^2+1)^2)

\int \frac{5 x ^{2} + 3 x + 5}{( x ^{2} + 1 ) ^{2}} d x

integral of e^{7x}sin(x)

\int e^{7 x} sin (x) d x

derivative of ln(3x^4)

\frac{d}{d x} (ln (3 x^{4}))

integral of x^3(8^{-x^4})

\int x^{3} (8^{- x^{4}}) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(2x+5)/(x-1) ?
The derivative of f(x)=(2x+5)/(x-1) is -7/((x-1)^2)
What is the first derivative of f(x)=(2x+5)/(x-1) ?
The first derivative of f(x)=(2x+5)/(x-1) is -7/((x-1)^2)