What is the derivative of ((3x+5)/((2x-6))) ?

The derivative of ((3x+5)/((2x-6))) is -7/((x-3)^2)

What is the first derivative of ((3x+5)/((2x-6))) ?

The first derivative of ((3x+5)/((2x-6))) is -7/((x-3)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{( 3 x + 5 )}{( 2 x - 6 )})

- \frac{7}{( x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 3 x + 5 )}{( 2 x - 6 )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x + 5 ) ( 2 x - 6 ) - \frac{d}{d x} ( 2 x - 6 ) ( 3 x + 5 )}{( 2 x - 6 ) ^{2}}

\frac{d}{d x} (3 x + 5) = 3

\frac{d}{d x} (2 x - 6) = 2

= \frac{3 ( 2 x - 6 ) - 2 ( 3 x + 5 )}{( 2 x - 6 ) ^{2}}

Simplify

\frac{3 ( 2 x - 6 ) - 2 ( 3 x + 5 )}{( 2 x - 6 ) ^{2}} : - \frac{7}{( x - 3 ) ^{2}}

= - \frac{7}{( x - 3 ) ^{2}}

f (x) = (x^{3} - \frac{4}{x})^{- 6}

\frac{d}{d x} (arcsin (ln (k x + 9)))

\int 2 e^{- t} t d t

\int e^{- 10 r^{2}} d r

(x - 1) \cdot ln (x - 1), 2

What is the derivative of ((3x+5)/((2x-6))) ?
The derivative of ((3x+5)/((2x-6))) is -7/((x-3)^2)
What is the first derivative of ((3x+5)/((2x-6))) ?
The first derivative of ((3x+5)/((2x-6))) is -7/((x-3)^2)