What is the derivative of y=(4x^4+5)/(x^2) ?

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

What is the first derivative of y=(4x^4+5)/(x^2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{4 x ^{4} + 5}{x ^{2}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (4 x^{4} + 5) = 16 x^{3}

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

= \frac{16 x ^{3} x ^{2} - 2 x ( 4 x ^{4} + 5 )}{( x ^{2} ) ^{2}}

Simplify

\frac{16 x ^{3} x ^{2} - 2 x ( 4 x ^{4} + 5 )}{( x ^{2} ) ^{2}} : \frac{2 ( 4 x ^{4} - 5 )}{x ^{3}}

= \frac{2 ( 4 x ^{4} - 5 )}{x ^{3}}

\frac{\partial}{\partial x} (4 - 2 x^{2} - y^{2})

\frac{d}{d x} (e^{- b x^{2}})

y = x^{2} - 3 x + 3 (0.3)

\frac{1}{s ( s ^{2} + 49 )}

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

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