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

1 Answer

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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


User JosephHirn
by
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