What is the derivative of (5x^4+7x^2-3/(2x^2)) ?

The derivative of (5x^4+7x^2-3/(2x^2)) is (5x^4+3)/(x^3)

What is the first derivative of (5x^4+7x^2-3/(2x^2)) ?

The first derivative of (5x^4+7x^2-3/(2x^2)) is (5x^4+3)/(x^3)

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{5 x ^{4} + 7 x ^{2} - 3}{2 x ^{2}})

\frac{5 x ^{4} + 3}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{5 x ^{4} + 7 x ^{2} - 3}{2 x ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} (\frac{5 x ^{4} + 7 x ^{2} - 3}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( 5 x ^{4} + 7 x ^{2} - 3 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 5 x ^{4} + 7 x ^{2} - 3 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (5 x^{4} + 7 x^{2} - 3) = 20 x^{3} + 14 x

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

= \frac{1}{2} \cdot \frac{( 20 x ^{3} + 14 x ) x ^{2} - 2 x ( 5 x ^{4} + 7 x ^{2} - 3 )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{( 20 x ^{3} + 14 x ) x ^{2} - 2 x ( 5 x ^{4} + 7 x ^{2} - 3 )}{( x ^{2} ) ^{2}} : \frac{5 x ^{4} + 3}{x ^{3}}

= \frac{5 x ^{4} + 3}{x ^{3}}

\int 4 x e^{x^{2}} d x

\int 3 y e^{3 z} d z

\int (x + \frac{1}{8 x}) d x

\int \frac{12}{x} d x

ln (x^{4} + x)

What is the derivative of (5x^4+7x^2-3/(2x^2)) ?
The derivative of (5x^4+7x^2-3/(2x^2)) is (5x^4+3)/(x^3)
What is the first derivative of (5x^4+7x^2-3/(2x^2)) ?
The first derivative of (5x^4+7x^2-3/(2x^2)) is (5x^4+3)/(x^3)