Ok, so I found my mistakes
(1/y)(dy/dx) = ((x)(-1/x) - (ln(2/x))(1))/x²
(1/y)(dy/dx) = (-1 - ln2 + lnx)/x²
dy/dx = y(-1 - ln2 + lnx)/x²
And if I can't leave y in my answer, I substituted y back in as
dy/dx = ((2/x)^(1/x)(-1 - ln2 + lnx))/x²
Should I factor in the (2/x)^(1/x) or leave...
Ok so by using implicit differentiation and simplifying ln(2/x) as ln2 - lnx, I get
(1/y)(dy/dx) = ((x)(0-1/x) - (ln2-lnx)(1))/x
(1/y)(dy/dx) = (-x - ln2 - lnx)/x²
dy/dx = y(-x - ln2 - lnx)/x²
And my final answer turns out
dy/dx = (-xy - yln2 - ylnx)/x²
Did I do something wrong? It...
Homework Statement
Find (2/x)^(1/x). Simplify your answer.
Homework Equations
The Attempt at a Solution
I let y = (2/x)^(1/x)
lny = ln(2/x)^(1/x)
lny= ln(2/x)/x
However, I get stuck here and don't know whether I should use e on both sides to get y by itself or to use implicit...