en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=(2x+3)/(5x-1)

Solution

derivative of

y = \frac{2 x + 3}{5 x - 1}

Solution

- \frac{17}{( 5 x - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (5 x - 1) = 5

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

Simplify

\frac{2 ( 5 x - 1 ) - 5 ( 2 x + 3 )}{( 5 x - 1 ) ^{2}} : - \frac{17}{( 5 x - 1 ) ^{2}}

= - \frac{17}{( 5 x - 1 ) ^{2}}

Popular Examples

derivative of y=-2(x+1)^2-4 derivative of

y = - 2 (x + 1)^{2} - 4

limit as x approaches 4+of 3/(x^2-16)

x \to 4 + lim (\frac{3}{x ^{2} - 16})

(\partial)/(\partial x)(4e^{xy+2})

\frac{\partial}{\partial x} (4 e^{x y + 2})

inverse oflaplace ((2s+6))/(s^2+9)inverse laplace

\frac{( 2 s + 6 )}{s ^{2} + 9}

derivative of f(x)=-8x^3-52x^2+3 derivative of

f (x) = - 8 x^{3} - 52 x^{2} + 3

Frequently Asked Questions (FAQ)

What is the derivative of y=(2x+3)/(5x-1) ?
The derivative of y=(2x+3)/(5x-1) is -(17)/((5x-1)^2)
What is the first derivative of y=(2x+3)/(5x-1) ?
The first derivative of y=(2x+3)/(5x-1) is -(17)/((5x-1)^2)