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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

integral of cot^5(θ)sin^4(θ)

\int cot^{5} (θ) sin^{4} (θ) d θ

limit as x approaches 0 of x^6cos(7/x)

x \to 0 lim (x^{6} cos (\frac{7}{x}))

derivative of (16cx-4x^2^{1/2})

\frac{d}{d x} ((16 c x - 4 x^{2})^{\frac{1}{2}})

limit as x approaches 0 of x^4-(x^3)/3

x \to 0 lim (x^{4} - \frac{x ^{3}}{3})

area y=3x^2,y=18x-27,[0,3]area

y = 3 x^{2}, y = 18 x - 27, [0, 3]

Frequently Asked Questions (FAQ)

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