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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

e^y*((dy)/(dx)+1)=1

e^{y} \cdot (\frac{d y}{d x} + 1) = 1

y^{''}+3y^'+10y=0

y^{^{''}} + 3 y^{^{'}} + 10 y = 0

slope of (-6,-6),(-5,0)slope

(- 6, - 6), (- 5, 0)

integral of 16cos^2(x+3)sin^2(x+3)

\int 16 cos^{2} (x + 3) sin^{2} (x + 3) d x

derivative of x^3+5x^2-x^{-2}+8

\frac{d}{d x} (x^{3} + 5 x^{2} - x^{- 2} + 8)

Frequently Asked Questions (FAQ)

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