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

The derivative of (4x^5+5)/(x^3) is (8x^5-15)/(x^4)

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

The first derivative of (4x^5+5)/(x^3) is (8x^5-15)/(x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{8 x ^{5} - 15}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (4 x^{5} + 5) = 20 x^{4}

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

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

Simplify

\frac{20 x ^{4} x ^{3} - 3 x ^{2} ( 4 x ^{5} + 5 )}{( x ^{3} ) ^{2}} : \frac{8 x ^{5} - 15}{x ^{4}}

= \frac{8 x ^{5} - 15}{x ^{4}}

y^{^{'}} = x y^{2}

\frac{d}{d x} (e^{x} sin (x) cos (x))

\frac{d}{d x} (\frac{1}{x} + \frac{1}{y})

y^{^{''}} + (y^{^{'}})^{2} = 0

7 cos (7 x), 7 - 7 cos (7 x), [0, \frac{π}{7}]

What is the derivative of (4x^5+5)/(x^3) ?
The derivative of (4x^5+5)/(x^3) is (8x^5-15)/(x^4)
What is the first derivative of (4x^5+5)/(x^3) ?
The first derivative of (4x^5+5)/(x^3) is (8x^5-15)/(x^4)