What is the derivative of f(x)=(8x^2+8x+2)/(sqrt(x)) ?

The derivative of f(x)=(8x^2+8x+2)/(sqrt(x)) is (12x^2+4x-1)/(xsqrt(x))

What is the first derivative of f(x)=(8x^2+8x+2)/(sqrt(x)) ?

The first derivative of f(x)=(8x^2+8x+2)/(sqrt(x)) is (12x^2+4x-1)/(xsqrt(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{8 x ^{2} + 8 x + 2}{x}

\frac{12 x ^{2} + 4 x - 1}{x x}

Solution steps

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 2}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (8 x^{2} + 8 x + 2) = 16 x + 8

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{( 16 x + 8 ) x - \frac{1}{2 x} ( 8 x ^{2} + 8 x + 2 )}{( x ) ^{2}}

Simplify

\frac{( 16 x + 8 ) x - \frac{1}{2 x} ( 8 x ^{2} + 8 x + 2 )}{( x ) ^{2}} : \frac{12 x ^{2} + 4 x - 1}{x x}

= \frac{12 x ^{2} + 4 x - 1}{x x}

\frac{( s )}{( s - 1 ) ^{2}}

\int x^{2} sin (2 x) d x

\frac{d}{d x} ((a x^{2} + b x + c) e^{\frac{- x}{6}})

x \to 7 lim (\frac{5 x}{x + 2})

t \to - 2 lim (t^{2} - 6 t - 16)

What is the derivative of f(x)=(8x^2+8x+2)/(sqrt(x)) ?
The derivative of f(x)=(8x^2+8x+2)/(sqrt(x)) is (12x^2+4x-1)/(xsqrt(x))
What is the first derivative of f(x)=(8x^2+8x+2)/(sqrt(x)) ?
The first derivative of f(x)=(8x^2+8x+2)/(sqrt(x)) is (12x^2+4x-1)/(xsqrt(x))