Examples

So one thing divided by another.

2

3

2 4x

x

y = u/v To differentiate use the formula

2

du dvv -udy dx dx=

dx v

2du

xdx

u = x2 - 5

v= 2x2

4dv

xdx

2 2

2 2

(2 )(2 ) ( 5)(4 )

(2 )

dy x x x x

dx x

3 3

4

4 4 20

4

dy x x x

dx x

3

5dy

dx x

2

2

x -5y=

2x

1Differentiate with respect to x.

2+5x

u=1

du=0

dx

v=2+5x

dv=5

dx

2 2

dy (2+5x)0-1(5) -5= =

dx (2+5x) (2+5x)

3

3

4

2

1.2 4

2 32.

4cos

3.

4.3 13 3

5.

sin6.

2

xy

x

x xy

xx

yx

xy

xx

txx

yx