What is the derivative of (1/(y^2)-9/(y^4))(y+7y^3) ?

The derivative of (1/(y^2)-9/(y^4))(y+7y^3) is (62)/(y^2)+(27)/(y^4)+7

What is the first derivative of (1/(y^2)-9/(y^4))(y+7y^3) ?

The first derivative of (1/(y^2)-9/(y^4))(y+7y^3) is (62)/(y^2)+(27)/(y^4)+7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(\frac{1}{y ^{2}} - \frac{9}{y ^{4}}) (y + 7 y^{3})

\frac{62}{y ^{2}} + \frac{27}{y ^{4}} + 7

Solution steps

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{9}{y ^{4}}) (y + 7 y^{3}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{y ^{2}} - \frac{9}{y ^{4}}, g = y + 7 y^{3}

= \frac{d}{d y} (\frac{1}{y ^{2}} - \frac{9}{y ^{4}}) (y + 7 y^{3}) + \frac{d}{d y} (y + 7 y^{3}) (\frac{1}{y ^{2}} - \frac{9}{y ^{4}})

\frac{d}{d y} (\frac{1}{y ^{2}} - \frac{9}{y ^{4}}) = - \frac{2}{y ^{3}} + \frac{36}{y ^{5}}

\frac{d}{d y} (y + 7 y^{3}) = 1 + 21 y^{2}

= (- \frac{2}{y ^{3}} + \frac{36}{y ^{5}}) (y + 7 y^{3}) + (1 + 21 y^{2}) (\frac{1}{y ^{2}} - \frac{9}{y ^{4}})

Simplify

(- \frac{2}{y ^{3}} + \frac{36}{y ^{5}}) (y + 7 y^{3}) + (1 + 21 y^{2}) (\frac{1}{y ^{2}} - \frac{9}{y ^{4}}) : \frac{62}{y ^{2}} + \frac{27}{y ^{4}} + 7

= \frac{62}{y ^{2}} + \frac{27}{y ^{4}} + 7

\int - 8 sin (x) d x

\int \frac{x ^{2} - x + 8}{x ^{3} + 2 x} d x

\int (x + 1) (3 x + 2) d x

f (x) = x^{3} - 12 x

\int (\frac{3}{5}) cos (x) d x

What is the derivative of (1/(y^2)-9/(y^4))(y+7y^3) ?
The derivative of (1/(y^2)-9/(y^4))(y+7y^3) is (62)/(y^2)+(27)/(y^4)+7
What is the first derivative of (1/(y^2)-9/(y^4))(y+7y^3) ?
The first derivative of (1/(y^2)-9/(y^4))(y+7y^3) is (62)/(y^2)+(27)/(y^4)+7