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Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Solution
y = e-x logx = uv (say)
Here u = e-x and v = log x
⇒ u’ = -e-x and v’ = `1/x`
Now y = uv
⇒ y’ = uv’ + vu’
(i.e.) `("d"y)/("d"x) = "e"^-x (1/x) + log x(-"e"^-x)`
`("d"y)/("d"x) = "e"^-x (1/x - log x)`
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