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Find the derivative of the inverse function of the following : y = x2·ex - Mathematics and Statistics

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प्रश्न

Find the derivative of the inverse function of the following : y = x2·ex 

बेरीज

उत्तर

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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Derivatives of Inverse Functions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Differentiation - Exercise 1.2 [पृष्ठ २९]

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