en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x^2/(3x-1))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

Expand

2 x (3 x - 1) - 3 x^{2} : 3 x^{2} - 2 x

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

Popular Examples

(\partial)/(\partial x)(8^x)

\frac{\partial}{\partial x} (8^{x})

integral from 1 to sqrt(x of) 1/(1+t^2)

\int_{1}^{x} \frac{1}{1 + t ^{2}} d t

derivative of e^x(3x^2-5x)derivative of

e^{x} (3 x^{2} - 5 x)

(dy)/(dx)=((-y^2))/((1+y^2))*(e^{-x})

\frac{d y}{d x} = \frac{( - y ^{2} )}{( 1 + y ^{2} )} \cdot (e^{- x})

derivative of-2sin(x-xcos(x))

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

Frequently Asked Questions (FAQ)

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