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Popular >

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

Solution

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

Solution

- \frac{4}{( x - 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{4}{( x - 3 ) ^{2}}

Popular Examples

derivative of y=arcsin(6x+1)derivative of

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(d^3)/(dx^3)(3n^{-1/3}+2n^{5/3})

\frac{d ^{3}}{d x ^{3}} (3 n^{- \frac{1}{3}} + 2 n^{\frac{5}{3}})

integral of 1/(sqrt(-2x^2-12x+32))

\int \frac{1}{- 2 x ^{2} - 12 x + 32} d x

3t(dy)/(dt)+y=t^4

3 t \frac{d y}{d t} + y = t^{4}

derivative of ln((e^x)/(1+e^x))derivative of

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Frequently Asked Questions (FAQ)

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