Question

what is the derivative of pi^x

Answer 1

@xapproachesinfinity @myininaya

Answer 2

in general
\[\frac{d}{dx} a^x = \ln(a) a^x\]

Answer 3

can you explain that a little more @dumbcow

Answer 4

thats a direct formula
you may simply replace \(a\) by \(\pi\)

Answer 5

so that is like a theorem?

Answer 6

do you know the derivative of e^x ?

Answer 7

e^x

Answer 8

Very good! what about the derivative of \(\large e^{5x}\) ?

Answer 9

e^5x (5)

Answer 10

yeah

Answer 11

so you do know chain rule, nice :) now you can use those two result to find the derivative of \(\pi^x \)

Answer 12

e^(5x)* (5)

Answer 13

see if you can write \(\pi^x\) as a power of \(e\)

Answer 14

but where does the ln come from?

Answer 15

ln and e are lovers

Answer 16

we rewrite in another form because we know how to take the derivative of it

Answer 17

ohhh that makes so much sense...thanks so much!!