Question

if $e^y+xy=e$ , then the value of $\frac{d^{2y} }{dx^{2} }$ is

Answer 1

Given :- d(e^y + xy)dx =d( e )/dx

e^y *dy/dx + d(xy)/dx =0

e^y y' + d(x)/dx + dy/dx =0

e^y y' + 1 + y'=0

y'(e^y +1 ) = -1

y' = -1/(e^y+1)

y' = -1 (e^y+1)^-1

using chin rule :- y = f'(g(x)*((g'(x)))

y" = (e^y +1)^-2 * d(e^y)/dx

y" = e^y ×y'/(e^y+1)

d²y/dx² = e^ydy/dx/(e^y+1) Answer

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Answer 2

Answer:

refer to this attachment ✅✅