Question is: Evaluate the following limits lim x--> 0 4^x - e^2x / 2x So i take derivatives but thats where im confused.... Whats the derivate of 4^x... x4^-x??? and is the derivative of -e^2x -2e^x??? So then that leaves me with 4x^-x -2e^x /2which is 0... so do i do derivatives again??? It seems like the x's wont go away????
You can use the chain rule and the fact that the derivative of e^x is e^x to answer both questions. That is, the derivative of e^f(x) is e^f(x)*f'(x). Try to rewrite 4^x as e^f(x). (use logs)
[tex]f(x)=4^x[/tex] [tex]\ln(f(x))=x\ln(4)[/tex] [tex]\frac{1}{f(x)}*f'(x)=\ln(4)[/tex] You can take it from there.