# l'Hopitals Rule... need help with derivatives?

by m0286
Tags: derivatives, lhopitals, rule
 P: 63 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????
 HW Helper P: 2,566 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)
 P: 789 $$f(x)=4^x$$ $$\ln(f(x))=x\ln(4)$$ $$\frac{1}{f(x)}*f'(x)=\ln(4)$$ You can take it from there.

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