Question

How do you find the maclaurin series for 10^x?

Answer 1

\[\sum_{n=1}^{\infty}\frac{f^n(0)x^n}{n!}\]

Answer 2

start taking the derivatives

Answer 3

Like f'(x) = x10^(x-1)?

Answer 4

f^1 = ln(10)*10^x
f^2 = ln^2(10)10^x
....
so the derivatives at x = 0 are
ln(10)
ln(10)^2
ln(10)^3
so the maclorian is
\[\sum_{n=1}^{\infty}\frac{(ln(10)x)^n}{n!}\]

Answer 5

No, that's not correct. The power rule applies for
\[\frac{ d }{ dx }x^n\]
but
\[\frac{ d }{ dx } 10^x\]
is something quite different! Learn how to differentiate exponential functions.

Answer 6

no
derivative of a^x = ln(a)*a^x

Answer 7

don't worry everyone forgets how to differentiate that....common mistake to confuse it with a power rule.

Answer 8

Thanks, so then, thats it?

Answer 9

that was confusing;p

Answer 10

d/dx e^x
is the same
ln(e)*e^x = 1*e^x = e^x

Answer 11

so proving a^x with e^x does not help:P

Answer 12

just memorize it

Answer 13

I don't think I can forget it now, thanks!