Find the derivatives for the following questions: a) y=x^lnx b) y=(1+x)^1/x c) y=((x-1)^2e^2x)/((x^2+1)^2(x^3-10)^3)
Derivatives for exponential equations, the natural logarithm and derivative rules
The Attempt at a Solution
For a) I came up with an answer of (x^lnxlnx)/x, however, this is not the correct answer as it should be 2(lnx)x^lnx-1. I know where the x^lnx-1 came from, I am just lost on how that 2 got there.
b) is much the same as a) for me, as my answer of -((1+x)^1/xln(1+x))/x^2 is not close to the correct answer of (((1+x)^1/x)/x^2)((x/(1+x))-ln(1+x)). I don't know if my problems here are stemming from simplification or if I simply overlooked something when solving.
For c), basically I have no idea how to solve this one :tongue: My first try was to use the quotient rule, but this resulted in a HUGE amount of work, and got me thinking that there might be an easier way to solve it. Is there an easier way to solve this question, or is the quotient rule the only way to go about it?
Any help you guys can give for these questions will be greatly appreicated, thanks in advance.