Differentiate: (product rule)?

Question

1. Y= X^2 ( 2X + 3 )

2. Y= X^2 ( X + 1 )^3

3. Y= ( X^3 + 5X^2 - 3 )( X^2 - 1 )^5

4. Y= ( 5X + 3 )( X - 7)^-1/3

5. Y= ( 2X + 9 ) √(X^2 - 4)

Answer 1

The product rule is this:

"If y=uv

then (dy/dx)=u(dv/dx)+v(du/dx)"

Now do your homework yourself.

Answer 2

Do your own HW, kid.

I'll help with 1.

1. y'=2x(2x+3)+2x^2

    y'=2x(4x+3)

Answer 3

The product rule is dy/dx = uv' + vu'

For 1. y = x²(2x + 3)

u = x²

u' = 2x

v = 2x + 3

v' = 2

So, using the product rule

dy/dx x²(2x + 3) = uv' + vu'

= 2x² + 2x(2x + 3)

= 2x² + 4x² + 6x

= 6x² + 6x

Try working the rest out yourself :)