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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of 3/(x^6)

\int \frac{3}{x ^{6}} d x

tangent of y=x^2-2x-2,(3,1)tangent of

y = x^{2} - 2 x - 2, (3, 1)

integral of 1/2 (3sin(x)+7)

\int \frac{1}{2} (3 sin (x) + 7) d x

derivative of y=2x(5-3x)^4 derivative of

y = 2 x (5 - 3 x)^{4}

limit as x approaches 0 of (sec(x))/x

x \to 0 lim (\frac{sec ( x )}{x})

Frequently Asked Questions (FAQ)

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