Derivative of e

[neutron star]

1. The problem statement, all variables and given/known data
Find the derivative of the given function
z=(te^6t + e^7t)^5


2. Relevant equations



3. The attempt at a solution
5(te^6t + e^7t)^4

[Dick]

That's wrong! Chain rule! Then product rule!

[lurflurf]

write
z=(te^6t + e^7t)^5=(t+e^t)^5*e^30t

[Dick]

write
z=(te^6t + e^7t)^5=(t+e^t)e^30t

You mean z=(t+e^t)^5*e^30t. And I don't see how that makes it easier. The original form for z is easy enough to differentiate if you use the rules.

[lurflurf]

They are both easy, but I thought the use of slightly fewer rules was an improvement.
(te^6t + e^7t)^5
power rule with chain rule
sum rule
product rule
derivative of an exponential with chain rule x2
derivative of the variable
total=9 rules (3 chain)
vs
(t+e^t)^5*e^30t
product rule
derivative of an exponential with chain rule
power rule with chain rule
sum rule
derivative of the variable
derivative of an exponential
total=8 rules (2 chain)
Though most important
(t+e^t)^5*e^30t is more aesthetically pleasing to my eye.

[Dick]

Well, now it's up to neutron star to pull off either one.