What is the derivative of y=(3x^5+7)/(x^3) ?

The derivative of y=(3x^5+7)/(x^3) is (3(2x^5-7))/(x^4)

What is the first derivative of y=(3x^5+7)/(x^3) ?

The first derivative of y=(3x^5+7)/(x^3) is (3(2x^5-7))/(x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{3 x ^{5} + 7}{x ^{3}}

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

Solution steps

\frac{d}{d x} (\frac{3 x ^{5} + 7}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x ^{5} + 7 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( 3 x ^{5} + 7 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (3 x^{5} + 7) = 15 x^{4}

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

= \frac{15 x ^{4} x ^{3} - 3 x ^{2} ( 3 x ^{5} + 7 )}{( x ^{3} ) ^{2}}

Simplify

\frac{15 x ^{4} x ^{3} - 3 x ^{2} ( 3 x ^{5} + 7 )}{( x ^{3} ) ^{2}} : \frac{3 ( 2 x ^{5} - 7 )}{x ^{4}}

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

t^{2} \frac{d x}{d t} = 2 t x + 1

\int \frac{1}{x ^{2} ( 1 + \frac{1}{x} ) ^{3}} d x

\frac{d}{d x} (2 x^{3} - 3 x^{2} - 36 x + 5)

\int_{0}^{1} 5 x^{4} e^{- x} d x

\int \frac{4}{x ^{2} - 14 x + 49} d x

What is the derivative of y=(3x^5+7)/(x^3) ?
The derivative of y=(3x^5+7)/(x^3) is (3(2x^5-7))/(x^4)
What is the first derivative of y=(3x^5+7)/(x^3) ?
The first derivative of y=(3x^5+7)/(x^3) is (3(2x^5-7))/(x^4)