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Question
Find the derivative of the inverse function of the following : y = x2·ex
Solution
y = x2·ex
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(x^2.e^x)`
= `x^2"d"/"dx"(e^x) + e^x"d"/"dx"(x^2)`
= x2·ex + ex x 2x
= xex (x + 2)
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(xe^x(x + 2)`.
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