en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x-3/(2x-5))

Solution

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

Solution

\frac{1}{( 2 x - 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (2 x - 5) = 2

= \frac{1 \cdot ( 2 x - 5 ) - 2 ( x - 3 )}{( 2 x - 5 ) ^{2}}

Simplify

\frac{1 \cdot ( 2 x - 5 ) - 2 ( x - 3 )}{( 2 x - 5 ) ^{2}} : \frac{1}{( 2 x - 5 ) ^{2}}

= \frac{1}{( 2 x - 5 ) ^{2}}

Popular Examples

derivative of-x^2sin(x+4xcos(x)+2sin(x))

\frac{d}{d x} (- x^{2} sin (x) + 4 x cos (x) + 2 sin (x))

derivative of sqrt(ln(x^2+4)+xsin(2x))derivative of

ln (x^{2} + 4) + x sin (2 x)

derivative of 6x^2+8x+6

\frac{d}{d x} (6 x^{2} + 8 x + 6)

integral of x^{15}e^{-x^8}

\int x^{15} e^{- x^{8}} d x

integral of (2x+5)(x^2+5x)^7

\int (2 x + 5) (x^{2} + 5 x)^{7} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x-3/(2x-5)) ?
The derivative of (x-3/(2x-5)) is 1/((2x-5)^2)
What is the first derivative of (x-3/(2x-5)) ?
The first derivative of (x-3/(2x-5)) is 1/((2x-5)^2)