find the derivative?

Question

g(w)=e^w(5w^2+3w+1)

Answer 1

You can also distribute the e^w to all the terms in parenthesis, then use power rule.  This could make it a bit easier to find the derivative.

 

g(w) = 5w²e^w + 3we^w + e^w

 

 

Use power rule.  You may also apply product rule to some of these terms.

 

g'(w) = (10we^w + 5w²e^w) + (3e^w + 3we^w) + e^w

 

 

Now just combine like terms.

 

g'(w) = 5w²e^w + 13we^w + 4e^w

Answer 2

Here we must use product rule first because e^w is being multiplied by 5w^2+3w+1,

 

so u=e^w and v=5w^2+3w+1 ------> u'=e^w and v'=10w+3

 

the equation for product rule is u'v+v'u

 

therefore the derivative (g'(w))= e^w(5w^2+3w+1)+(10w+3)e^w

 

If you have any questions, I'd recommend trying out an online session with me. Best of luck!