Question

differentiate log x 3^x

Answer 1

is that \[3^xlog x\]?

Answer 2

yes

Answer 3

you will need to use the product rule for this.
y'=u'v+v'u
are you familiar with this?

Answer 4

how would you dash 3^x?

Answer 5

here is the method, a little trick is used to make it easier

http://www.math.com/tables/derivatives/more/b%5Ex.htm

Answer 6

i don't understand =(

Answer 7

okay lets just look as the derivative of 3^x

\[3^x \frac{d}{dx} = e^{ln3^x} \frac{d}{dx}\]
\[=e^{xln3} \frac{d}{dx}\]

Now let u =xln3 then x=u/ln3

\[=e^{u} ln3\frac{d}{du}\]\[=ln3e^{u} \]\[=ln3e^{xln3} \]\[=ln3e^{ln3^x} \]\[=(ln3)3^x \]

Answer 8

Differential of a^x= a^x lna