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

The derivative of (1-x^2+x^4)/(x^2*sqrt(x)) is (3x^4+x^2-5)/(2x^{7/2)}

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

The first derivative of (1-x^2+x^4)/(x^2*sqrt(x)) is (3x^4+x^2-5)/(2x^{7/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{2} x) = 2 x x + \frac{x ^{\frac{3}{2}}}{2}

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

Simplify

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

= \frac{3 x ^{4} + x ^{2} - 5}{2 x ^{\frac{7}{2}}}

x \to 0 lim (\frac{0}{0})

f (t) = (4 t^{2} - 8 t + 7)^{\frac{3}{2}}

\int \frac{2 x ^{2} + x - 1}{2 x ^{3} + x ^{2} - 5 x + 2} d x

\int \frac{x - 1}{x ^{2} - 4} d x

\int \frac{9}{x ^{2} - 16} d x

What is the derivative of (1-x^2+x^4)/(x^2*sqrt(x)) ?
The derivative of (1-x^2+x^4)/(x^2*sqrt(x)) is (3x^4+x^2-5)/(2x^{7/2)}
What is the first derivative of (1-x^2+x^4)/(x^2*sqrt(x)) ?
The first derivative of (1-x^2+x^4)/(x^2*sqrt(x)) is (3x^4+x^2-5)/(2x^{7/2)}