How do you find the second derivative of g(t)=t^(3) e^(5t) ? I already found the first derivative which is g'(t)=t^(2)e^(5t)[5t+3] but how do you find the derivative for the second one?

Question

anonymous · Answer

Do you use the product rule?

mathstudent55 · Answer

Your first derivative is correct.
I would distribute t^2e^(5t) and get a sum of two terms.
Then differentiate the sum using the product rule for each term.

mathstudent55 · Answer

Another way is to distribute just t^2 and do as above.

mathstudent55 · Answer

g'(t) = e^(5t)(5t^3 + 3t^2)
Now use the product rule.

anonymous · Answer

so I got g''(t)=te^(5t)[25t^(2)+30t+6] is that correct?

mathstudent55 · Answer

Yes, you are correct.
Good job!

anonymous · Answer

Thank you so much :D

mathstudent55 · Answer

You're welcome