Find the derivatives of the following functions with respect to corresponding independent variables: y = e-x . log x - Mathematics

Find the derivatives of the following functions with respect to corresponding independent variables:

y = e^-x . log x

योग

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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Differentiation Rules

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अध्याय 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.2 [पृष्ठ १६०]

अध्याय 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.2 | Q 16 | पृष्ठ १६०

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