What is the derivative of z=(te^6t + e^7t)^5?

[neutron star]

Homework Statement

Find the derivative of the given function
z=(te^6t + e^7t)^5

Homework Equations

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.