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2 x 3 20 X 46 x(x2 + 3x) So it is two things multiplied together.

( 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

The derivative of y=(x3+3x)(x2+6) equals

(x3+3x)(2x)+(x2+6)(3x2+3)

udv

dxv

du

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

Differentiate x (x+2) with respect to x.

2( 2)( 5 ), .dm

If m n n n finddn