What is the derivative of ##y## with respect to ##x## for ##y = 17^x##?

##y’=17^x*ln17##

The first step is to rewrite ##17^x## as something differentiable.

##y=17^x=e^(ln17^x)=e^(xln17)##

##e^(xln17) ## is differentiable since we can use the :

##d/dx(e^u)=e^u*u’##

Apply this to ##e^(xln17)##:

##y’=d/dx(e^(xln17))=e^(xln17)*d/dx(xln17)##

Two things to consider here:

##color(white)(sss)## ##e^(xln17)## is still equal to ##17^x##, we can rewrite it as such now that ##color(white)(sss)## we’ve differentiated.

##color(white)(sss)## ##d/dx(xln17)=ln17## ##color(white)(sss)## Remember, ##ln17## is just a constant. Don’t be fooled by it.

Thus,

##y’=17^x*ln17##