Question

Can anyone explain to me how to differentiate 10^x .. the derivative is 10^x*ln(10)

Answer 1

change the 10 to e^ln10 and then use the chain rule
so
the derivative of e^(ln10*x) is e^(ln10*x) * ln10 =10^x * ln (10)

Answer 2

Awesome, thanks.

Answer 3

\[y=10^x \]
Take natural log of both sides
\[\ln(y)=\ln(10^x)\]
Using properties of log namely ln(x^r)=rln(x)<-this law we can rewrite as
\[\ln(y)=x \ln(10)\]
Now differentiating both sides we receive
\[\frac{y'}{y}= \ln(10) \text{ note: remember (xc)'=(cx)'=c(x)'=c(1)=c (c is constant))}\]
multipliing both sides by y we receive
\[y'=y \ln(10)\]
but like omg y was 10^x
so
\[y'=10^x \ln(10)\]

Answer 4

id say to memorize a general rule for any base.

[B^x]' = B^x ln(B)

when the Base is "e" we get:

[e^x]' = e^x ln(e) , and since ln(e) = 1 it can be written as:
= e^x

Answer 5

hey myininaya, how did you get words to show up not stupid in your equation?

Answer 6

\text{words}

Answer 7

hmm, learn something new everyday.