How do we differentiate y=a^x when 'a' is an non zero real number
Firstly we must change it into a form we can deal with. To do this we take the natural log (ln) of both sides.ln(y)=ln(ax) ln(y)=x(ln(a)) using our rules of logsFrom here we differentiate. The differential of ln(f(x)) is [(d/dx)f(x)]/f(x)(dy/dx)/y=ln(a) differentiating from above rule and ln(a) is just a constant so d/dx xln(a)= ln(a)dy/dx=yln(a) times both sides by ydy/dx=(ax)(ln(a)) subbing in y=ax to get dy/dx in terms of x
