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Popular >

derivative of (3x+1/(x-1))

Solution

\frac{d}{d x} (\frac{3 x + 1}{x - 1})

Solution

- \frac{4}{( x - 1 ) ^{2}}

Solution steps

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

\frac{d}{d x} (3 x + 1) = 3

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

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

Simplify

\frac{3 ( x - 1 ) - 1 \cdot ( 3 x + 1 )}{( x - 1 ) ^{2}} : - \frac{4}{( x - 1 ) ^{2}}

= - \frac{4}{( x - 1 ) ^{2}}

Popular Examples

(\partial)/(\partial x)(e^xsin(x))

\frac{\partial}{\partial x} (e^{x} sin (x))

limit as n approaches infinity of (n^2+3)/(n^3sqrt(n)+n^{5/2)}

n \to \infty lim (\frac{n ^{2} + 3}{n ^{3} n + n ^{\frac{5}{2}}})

integral of (x^3+3x-2)/(x^2-x)

\int \frac{x ^{3} + 3 x - 2}{x ^{2} - x} d x

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\frac{d}{d x} (\frac{7}{x ^{7}})

integral from 1 to 8 of x^{-8/3}

\int_{1}^{8} x^{- \frac{8}{3}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (3x+1/(x-1)) ?
The derivative of (3x+1/(x-1)) is -4/((x-1)^2)
What is the first derivative of (3x+1/(x-1)) ?
The first derivative of (3x+1/(x-1)) is -4/((x-1)^2)