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anonymous
 5 years ago
how do i find the derivative of f(x) = e^(12x^2) + ln (3e^4x)?
anonymous
 5 years ago
how do i find the derivative of f(x) = e^(12x^2) + ln (3e^4x)?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i need the answer...my exam is tomorrow! please help :(

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do u need the method or just theanswer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok here it goes d/dx(e^(12x^2)) is 4xe^(12x^2) because d/dx(e^f(x)) is e^(x)*d/dx(f(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0here f(x) is 12x^2 therefore d/dx(12x^2) is 4x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then d/dx(ln(3e^4x) is 4e^4x/(3e^4x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0because d/dx(log(f(x)) is (1/f(x))*d/dxf(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0where f(x) is (3e^4x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the answer is 4xe^(12x^2)+4e^4x/(3e^4x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what theorem or rules apply to this type of problem?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first of all d/dx(a+b) is da/dx+db/dx where a is e^(12x^2) and b is ln(3e^4x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first of all d/dx(a+b) is da/dx+db/dx where a is e^(12x^2) and b is ln(3e^4x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Maybe this will help: the derivative of e ^ (stuff) = e ^ (stuff) * (derivative of that stuff) the derivative of ln (stuff) = 1/(stuff) * (derivative of that stuff)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And as dipin said, if you have the derivative of things added or subtracted, you just take each derivative as you come across it. So derivative of (A + B) = derivative of A + derivative of B

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's just a big ugly when you have to type these things instead of write them by hand. :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we just solve the e^stuff and ln^stuff and then add them?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i just get confused because of the logs, e's, and ln's.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you can just try to step back and see the overall structure of the question (ignoring the specific bits), sometimes that helps

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0one thing u have to remember is d/dx of e^x is e^x and d/dx of log x is 1/x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Once you know the derivative of e^(stuff) = e^(stuff) * (derivative of that stuff), then you can make the stuff as complicated as you want, and you still have a basic framework for solving the question. (Of course, assuming all the proper variables like the derivative we're taking is dy/dx and the function is expressed in terms of x (or x and y, if you're there yet))

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for example e^4x is e^4x*d/dx(4x) which is 4e^4x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You don't even have to remember d/dx e^x = e^x, if you don't want to, because if you follow the pattern, you'll get there anyway. e^x just the special case where the (stuff) is x. And the derivative of x = 1. So, you get e^x * 1 when you take the derivative with respect to x. That's the nice thing about following the rules. :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0And then, you just clean it up like dipin does, usually writing it cleanly and compactly

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0d/dx(12x^2) will be 2*2*x which is 4x and we have a e^(stuff) there

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh! can i still stuff you guys into my head during the exam? :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0anyways gud luck for ur exam.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha thanks for everything!
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