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( 10 63 2 2x 5x 6x) 3xdy
xdx
For example (x + 2) (x2 +3x) You could multiply it out x ( x2 +3x) +2(x2 +3x) = x3 + 3x2 + 2x2 + 6x =x3 + 5x2 + 6x
Now for an easier method!!!
Let u = x + 2 and v= x2 + 3x
d(uv) dv du=u +v
dx dx dx
1du
dx 2 3
dvx
dx
2( 2)(2 3) ( 3 )(1)dy
x x x xdx
=3x2+ 10x+6
If y=uv. Then use the formula
dy dv du=u +v
dx dx dx
'
'
Note if instead of y, you are given f(x),then f (x) is the derivative of f(x).
df(x)f (x)= .
dx
Let u = (2x-5) and v = (3x2 +6).
Use the formula
Then and
So
2du
dx 6
dvx
dx
2 2 2
2
(2 5)(6 ) (3 6)(2) 12 30 6 12
18 30 12
dyx x x x x x
dxdy
x xdx
d(uv) dv du=u +v
dx dx dx