How do you find the derivative of #y=(3x)( x + 2)#?

Answer 1

I found: #y'=6(x+1)#

You can use the Product Rule where if you have a function: #y=f*g# then #y'=f'g+fg'# and get: #y'=3(x+2)+3x*1=3x+6+3x=6(x+1)#

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Answer 2

Emilia Aguilar

To find the derivative of ( y = (3x)(x + 2) ), you can use the product rule of differentiation. The product rule states that if ( y = u \cdot v ), where ( u ) and ( v ) are functions of ( x ), then ( y' = u'v + uv' ). Applying the product rule:

( y' = (3x)'(x + 2) + (3x)(x + 2)' )

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

( y' = 3x + 6 + 3x )

( \boxed{y' = 6x + 6} )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.