What is the derivative of (4x^2-1/2 x/(9x+8)) ?

The derivative of (4x^2-1/2 x/(9x+8)) is (36x^2+64x-4)/((9x+8)^2)

What is the first derivative of (4x^2-1/2 x/(9x+8)) ?

The first derivative of (4x^2-1/2 x/(9x+8)) is (36x^2+64x-4)/((9x+8)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{4 x ^{2} - \frac{1}{2} x}{9 x + 8})

\frac{36 x ^{2} + 64 x - 4}{( 9 x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} - \frac{1}{2} x}{9 x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} - \frac{1}{2} x ) ( 9 x + 8 ) - \frac{d}{d x} ( 9 x + 8 ) ( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 ) ^{2}}

\frac{d}{d x} (4 x^{2} - \frac{1}{2} x) = 8 x - \frac{1}{2}

\frac{d}{d x} (9 x + 8) = 9

= \frac{( 8 x - \frac{1}{2} ) ( 9 x + 8 ) - 9 ( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 ) ^{2}}

Simplify

\frac{( 8 x - \frac{1}{2} ) ( 9 x + 8 ) - 9 ( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 ) ^{2}} : \frac{36 x ^{2} + 64 x - 4}{( 9 x + 8 ) ^{2}}

= \frac{36 x ^{2} + 64 x - 4}{( 9 x + 8 ) ^{2}}

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

\int (- x)^{2 n} d x

d er i v a t i v e f (x) = 2 t^{- \frac{3}{4}}

\int t e^{t^{2}} d t

\frac{d}{d x} (\frac{3 x ^{2} - 5 x - 2}{4 x + 12})

What is the derivative of (4x^2-1/2 x/(9x+8)) ?
The derivative of (4x^2-1/2 x/(9x+8)) is (36x^2+64x-4)/((9x+8)^2)
What is the first derivative of (4x^2-1/2 x/(9x+8)) ?
The first derivative of (4x^2-1/2 x/(9x+8)) is (36x^2+64x-4)/((9x+8)^2)