What is the derivative of (8x^2+2x+4/(sqrt(x))) ?

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

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

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

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{8 x ^{2} + 2 x + 4}{x})

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

Solution steps

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

\frac{d}{d x} (8 x^{2} + 2 x + 4) = 16 x + 2

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

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

Simplify

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

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

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

\int_{3}^{4} - x^{2} + 7 x - 12 d x

\int 9 x^{2} ln (x) d x

x \to 6 + lim (ln (x^{2} - 36))

y^{^{'}} + x y = x

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