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Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
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Solution
y = (x2 + 5) log(1 + x) e–3x
`("d"y)/("d"x) = (x^2 + 5) [log (1 + x)"e"^(-3x) (- 3) + "e"^(-3x) xx 1/(1 + x)] + log(1 + x) * "e"^(-3x) (2x)`
`("d"y)/("d"x) = (x^2 + 5) [- 3"e"^(-3x) log(1 - x) + ("e"^(-3x))/(1 + x)] + 2x "e"^(-3x) log(1 + x)`
`("d"y)/("d"x) = "e"^(-3x) [- 3(x^2 + 5) log(1 + x) + (x^2 + 5)/(1 + x)] + "e"^(-3x) 2x log(1 + x)`
`("d"y)/("d"x) = "e"^(- 3x) [- 3(x^2 + 5) log(1 + x) + (x^2 + 5)/(1 + x) + 2x log (1 + x)`
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