What is the derivative of y=(x^7-2x^4+14x)/(x^4) ?

The derivative of y=(x^7-2x^4+14x)/(x^4) is (3(x^6-14))/(x^4)

What is the first derivative of y=(x^7-2x^4+14x)/(x^4) ?

The first derivative of y=(x^7-2x^4+14x)/(x^4) is (3(x^6-14))/(x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = \frac{x ^{7} - 2 x ^{4} + 14 x}{x ^{4}}

\frac{3 ( x ^{6} - 14 )}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{x ^{7} - 2 x ^{4} + 14 x}{x ^{4}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{7} - 2 x^{4} + 14 x) = 7 x^{6} - 8 x^{3} + 14

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

= \frac{( 7 x ^{6} - 8 x ^{3} + 14 ) x ^{4} - 4 x ^{3} ( x ^{7} - 2 x ^{4} + 14 x )}{( x ^{4} ) ^{2}}

Simplify

\frac{( 7 x ^{6} - 8 x ^{3} + 14 ) x ^{4} - 4 x ^{3} ( x ^{7} - 2 x ^{4} + 14 x )}{( x ^{4} ) ^{2}} : \frac{3 ( x ^{6} - 14 )}{x ^{4}}

= \frac{3 ( x ^{6} - 14 )}{x ^{4}}

x \to 3 lim (\frac{( x ^{2} )}{x - 3})

d er i v a t i v e 0.002 x^{2} + 1.7 x + 60

\frac{d}{d x} ((x + csc (x^{3} + 3))^{- 3})

d er i v a t i v e y = \frac{e ^{x}}{8 x ^{4}}

n \to \infty lim (\frac{n ^{2}}{2 n - 1} sin (\frac{1}{n}))

What is the derivative of y=(x^7-2x^4+14x)/(x^4) ?
The derivative of y=(x^7-2x^4+14x)/(x^4) is (3(x^6-14))/(x^4)
What is the first derivative of y=(x^7-2x^4+14x)/(x^4) ?
The first derivative of y=(x^7-2x^4+14x)/(x^4) is (3(x^6-14))/(x^4)