# Calculus - Derivative of many exponents

1. Homework Statement
Find the derivative.

2. Homework Equations
h(t)= t^(pi^3)+(pi^3)^t+(pi)t^3

3. The Attempt at a Solution
- i know that pi is a constant (number) so when finding it's derivative, it will be something like, (2nd part= (pi^3)^t ) : ln pi (pi^3)^t * 3t
- 3rd part = (pi)t^3 : 3(pi)t^2

- But the part I'm most confused is the first part = t^(pi^3)
- Would it be : 3pi(t^pi^3)*3pi ?

p.s: first part doesnt have any parenthesis around in the equation ( t^pi^3)
and sorry for such a messy equations. This is my first time using this forum.

ANSWER: pi^3)t^(pi^3-1) + ln (pi^3)^t + 3(pi)t^2
but i dont know how to.. get that

Last edited:

tiny-tim
Homework Helper
welcome to pf!

hi jazxd! welcome to pf!

(have a pi: π and try using the X2 icon just above the Reply box )
- i know that pi is a constant (number) so when finding it's derivative, it will be something like, (2nd part= (pi^3)^t ) : ln pi (pi^3)^t * 3t

not quite

hint: rewrite (π3)t as (eln (π3))t = et(ln (π3))

alternatively as π3t = (eln π)3t = e3t(ln π)
- But the part I'm most confused is the first part = t^(pi^3)
- Would it be : 3pi(t^pi^3)*3pi ?

no … this is just tn with n = π3

hmm, i know n is a number so it would require ln but why also an e^ln ?
and doesnt e and ln cancel out @__@;
im sorry, im only a senior in high school, and these stuff gets me big time.

so can you briefly show me how to do these 3 parts ?
im more like, "if i see the answer (or the works) first, i get it afterward" type learner

tiny-tim
Homework Helper
hi jazxd!

(just got up :zzz: …)
hmm, i know n is a number so it would require ln but why also an e^ln ?

because you know how to differentiate et, but you don't know how to differentiate nt

(or, like me, even if you do know, you can't be sure you remember it right! )
and doesnt e and ln cancel out @__@;

yup! … that's why it works!

now try it yourself