Question

Find the derivative y’(x) implicitly.

Answer 1

Implicitly from \[e^{4y} -lny = 2x\] you would get \[4e^{4y}\frac{ dy }{ dx } - \frac{ 1 }{ y }\frac{ dy }{ dx } = 2\] Then you have to simplify it to get \[\frac{ dy }{ dx }(4e^{4y} -\frac{ 1 }{ y }) = 2\]\[\frac{ dy }{ dx } = \frac{ 2 }{ 4e^{4y} - \frac{ 1 }{ y } }\] This is an okay answer, but it can be simplified further, by taking out a factor of 1/y from the bottom and moving it to the top.\[\frac{ dy }{ dx } = \frac{ 2y }{ 4ye^{4y} - 1 }\] This is the most simplified answer :) Hope this helped.

Answer 2

ohh okay