2019-수학-가형-홀수-7¶
문제¶
풀이¶
from sympy import *
x = symbols('x')
y = Function('y')(x)
expr = exp(x)-x*exp(y)-y
eqn = diff(expr, x)
eqn
\[\displaystyle - x e^{y{\left(x \right)}} \frac{d}{d x} y{\left(x \right)} + e^{x} - e^{y{\left(x \right)}} - \frac{d}{d x} y{\left(x \right)}\]
roots = solve(eqn, diff(y, x, 1))
dydx = roots[0]
dydx
\[\displaystyle \frac{e^{x} - e^{y{\left(x \right)}}}{x e^{y{\left(x \right)}} + 1}\]
dydx.subs({x:0,y:1})
\[\displaystyle 1 - e\]