Calculus - Derivative of many exponents

  • Thread starter jazxd
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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
 
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Answers and Replies

  • #2
tiny-tim
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welcome to pf!

hi jazxd! welcome to pf! :smile:

(have a pi: π and try using the X2 icon just above the Reply box :wink:)
- 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 :redface:

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
 
  • #3
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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
 
  • #4
tiny-tim
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hi jazxd! :smile:

(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 :smile:

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

yup! … that's why it works! :biggrin:

now try it yourself :smile:
 

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