en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of (5+6x/(9-4x))

Solution

\frac{d}{d x} (\frac{5 + 6 x}{9 - 4 x})

Solution

\frac{74}{( 9 - 4 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 + 6 x}{9 - 4 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 + 6 x ) ( 9 - 4 x ) - \frac{d}{d x} ( 9 - 4 x ) ( 5 + 6 x )}{( 9 - 4 x ) ^{2}}

\frac{d}{d x} (5 + 6 x) = 6

\frac{d}{d x} (9 - 4 x) = - 4

= \frac{6 ( 9 - 4 x ) - ( - 4 ) ( 5 + 6 x )}{( 9 - 4 x ) ^{2}}

Simplify

\frac{6 ( 9 - 4 x ) - ( - 4 ) ( 5 + 6 x )}{( 9 - 4 x ) ^{2}} : \frac{74}{( 9 - 4 x ) ^{2}}

= \frac{74}{( 9 - 4 x ) ^{2}}

Graph

Popular Examples

derivative of f(1)=x+1/x

d er i v a t i v e f (1) = x + \frac{1}{x}

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

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

integral of (12)/(1+4x^2)

\int \frac{12}{1 + 4 x ^{2}} d x

derivative of \sqrt[3]{x^{9.6}}+2e^{1.3}

\frac{d}{d x} (3 x^{9.6} + 2 e^{1.3})

integral from 1 to 2 of (1/t-i)^2

\int_{1}^{2} (\frac{1}{t} - i)^{2} d t

Frequently Asked Questions (FAQ)

What is the derivative of (5+6x/(9-4x)) ?
The derivative of (5+6x/(9-4x)) is (74)/((9-4x)^2)
What is the first derivative of (5+6x/(9-4x)) ?
The first derivative of (5+6x/(9-4x)) is (74)/((9-4x)^2)