sbentleyaz sbentleyaz

25-10-2016
Mathematics

Answered

.

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

Verified Answer :

apologiabiology apologiabiology

25-10-2016

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

y=\(\frac{ \frac{1}{4}1-ln4 }{1^2}\)
y=\(\frac{ \frac{1}{4}-ln4 }{1}\)
y=\(\frac{1}{4}-2ln2\)

the slope is \(\frac{1}{4}-2ln2\)

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