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

The derivative of (5x^2/(3x-1)) is (5(3x^2-2x))/((3x-1)^2)

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

The first derivative of (5x^2/(3x-1)) is (5(3x^2-2x))/((3x-1)^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{5 x ^{2}}{3 x - 1})

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \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}}

= 5 \cdot \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

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

Simplify

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

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

\int \frac{1}{x 16 + x ^{2}} d x

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

\int x^{3} sin (n x) d x

x \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 0

\int_{3}^{5} \frac{x}{x ^{2} + 6 x + 13} d x

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