What is the derivative of f(x)=(5x^4-3x^3)/(x^5) ?

The derivative of f(x)=(5x^4-3x^3)/(x^5) is (-5x+6)/(x^3)

What is the first derivative of f(x)=(5x^4-3x^3)/(x^5) ?

The first derivative of f(x)=(5x^4-3x^3)/(x^5) is (-5x+6)/(x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{- 5 x + 6}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (5 x^{4} - 3 x^{3}) = 20 x^{3} - 9 x^{2}

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

= \frac{( 20 x ^{3} - 9 x ^{2} ) x ^{5} - 5 x ^{4} ( 5 x ^{4} - 3 x ^{3} )}{( x ^{5} ) ^{2}}

Simplify

\frac{( 20 x ^{3} - 9 x ^{2} ) x ^{5} - 5 x ^{4} ( 5 x ^{4} - 3 x ^{3} )}{( x ^{5} ) ^{2}} : \frac{- 5 x + 6}{x ^{3}}

= \frac{- 5 x + 6}{x ^{3}}

(\frac{x - 1}{x + 1})^{^{'}}

\int_{0}^{π} 3 sin (x) d x

\int_{1}^{6} π (x - 1) d x

\frac{d r}{d t} = 6 (t + 1)^{\frac{1}{2}}, r (0) = 0

(3.6) (5.1)

What is the derivative of f(x)=(5x^4-3x^3)/(x^5) ?
The derivative of f(x)=(5x^4-3x^3)/(x^5) is (-5x+6)/(x^3)
What is the first derivative of f(x)=(5x^4-3x^3)/(x^5) ?
The first derivative of f(x)=(5x^4-3x^3)/(x^5) is (-5x+6)/(x^3)