Question

.
If e^xy = 4, then what is dy/dx at the point (1, ln4)?

Answer 1

e^xy=4
ln both sides
xy=ln4
divide x
y=(ln4)/x
differentiate
quotient rule
y=
`( (1)/(4)x-1ln4 )/(x^2)`
input 1 for x


y=
`( (1)/(4)1-ln4 )/(1^2)`
y=
`( (1)/(4)-ln4 )/(1)`
y=
`(1)/(4)-2ln2`

the slope is
`(1)/(4)-2ln2`