Question

f(x)=2^x find the derivative

Answer 1

here's an example that maybe you can follow

suppose you are given y = 4^x

first take the ln of both sides \[\implies \ln y = x\ln 4\]
now you take the derivative of both sides
\[\implies \frac 1y y^\prime = \ln 4\]
cross multiply
\[\implies y^\prime = y\ln 4\]
subsittue y
\[\implies y^\prime = 4^x \ln 4\]
does that help?

Answer 2

or if you want to memorize formulas... \[\huge \frac{\text d}{\text {dx}} (a^\text x) = a^\text x \ln a\]

Answer 3

where a is a constant

Answer 4

Or..
\[\large log_e{y} = xlog_e4 => y = e^{xln4}\]
\[=> \large\frac{dy}{dx} = ln4*e^{xln4} => ln4*4^{x}\]