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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}}

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(\partial)/(\partial x)((x^2+2)(x^3+1))

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limit as x approaches-5+of (-1)/(x^2-25)

x \to - 5 + lim (\frac{- 1}{x ^{2} - 25})

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n = 2 \sum \infty \frac{( 3 ^{3 n} )}{2 ^{2 n - 2}}

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)