en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x-6/(3x-2))

Solution

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

Solution

\frac{16}{( 3 x - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 6) = 1

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

= \frac{1 \cdot ( 3 x - 2 ) - 3 ( x - 6 )}{( 3 x - 2 ) ^{2}}

Simplify

\frac{1 \cdot ( 3 x - 2 ) - 3 ( x - 6 )}{( 3 x - 2 ) ^{2}} : \frac{16}{( 3 x - 2 ) ^{2}}

= \frac{16}{( 3 x - 2 ) ^{2}}

Popular Examples

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

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

derivative of 1/2 ln(x^2+y^2)

\frac{d}{d x} (\frac{1}{2} ln (x^{2} + y^{2}))

(d^2)/(dx^2)(1/((x-1)^2))

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

integral of x^2e^{20x}

\int x^{2} e^{20 x} d x

sum from n=0 to infinity of (x-5)^n

n = 0 \sum \infty (x - 5)^{n}

Frequently Asked Questions (FAQ)

What is the derivative of (x-6/(3x-2)) ?
The derivative of (x-6/(3x-2)) is (16)/((3x-2)^2)
What is the first derivative of (x-6/(3x-2)) ?
The first derivative of (x-6/(3x-2)) is (16)/((3x-2)^2)