Question

Find the derivative of the inverse function of the following : y = x²·e^x 

Answer 1

y = x²·e^x 
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·e^x + e^x x 2x
= xe^x (x + 2)
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(xe^x(x + 2)`.