Question

If y=x^y then dy/dx=
a)\[\frac{y^2}{x(1+ln y)}\]
b)\[\frac{y^2}{x(1-lny)}\]
c)\[\frac{2x}{y(1+ln x)}\]
d)\[\frac{2y}{x(1+lny)}\]

Answer 1

can we do implicit? or cange over to logs?

Answer 2

we can do anything we like

Answer 3

y = x^y

log(y) = log(x^y)

log(y) = y log(x)

1/y y' = y' log(x) + y/x