What is expand (2(y*v))(dy*v+y*dv) ?

The solution to expand (2(y*v))(dy*v+y*dv) is 2v^2ydy+2vy^2dv

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2(yv))(dyv+y*dv)

expand

(2 (y \cdot v)) (d y \cdot v + y \cdot d v)

2 v^{2} y d y + 2 v y^{2} d v

Solution steps

(2 (y v)) (d y v + y d v)

= (2 (v y)) (v d y + y d v)

Apply the distributive law:

a (b + c) = ab + a c

a = (2 (y v)), b = d y v, c = y d v

= (2 (y v)) d y v + (2 (y v)) y d v

= v (2 (v y)) d y + y (2 (v y)) d v

Simplify

v (2 (v y)) d y + y (2 (v y)) d v : 2 v^{2} y d y + 2 v y^{2} d v

= 2 v^{2} y d y + 2 v y^{2} d v

\frac{arccosh ( e ^{- x} )}{e ^{- x}}

\frac{1}{( s + 9 ) ( s ^{2} + k ^{2} )}

\frac{x - 1}{( x + 1 ) ^{3}}

(3 x^{2} - 1) d x

- sin (t) θ (t - \frac{π}{2})

What is expand (2(y*v))(dy*v+y*dv) ?
The solution to expand (2(y*v))(dy*v+y*dv) is 2v^2ydy+2vy^2dv