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You entered:

e^-x^2=y

What you mean?

e^((-x)^2) = y
 
e^(-x^2) = y
 
e^(-x^2) = y

Plot e^-x^2=y

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The solution

You have entered [src] 
   2    
 -x     
E    = y
$$e^{- x^{2}} = y$$
Find derivative

    Examples of implicit functions

    Learn more about Implicit function

    The above examples also contain:

    • the modulus or absolute value: absolute(x) or |x|
    • square roots sqrt(x),
      cubic roots cbrt(x)
    • trigonometric functions:
      sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)
    • exponential functions and exponents exp(x)
    • inverse trigonometric functions:
      arcsine asin(x), arccosine acos(x), arctangent atan(x), arccotangent acot(x)
    • natural logarithms ln(x),
      decimal logarithms log(x)
    • hyperbolic functions:
      hyperbolic sine sh(x), hyperbolic cosine ch(x), hyperbolic tangent and cotangent tanh(x), ctanh(x)
    • inverse hyperbolic functions:
      hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x), hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)
    • other trigonometry and hyperbolic functions:
      secant sec(x), cosecant csc(x), arcsecant asec(x), arccosecant acsc(x), hyperbolic secant sech(x), hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x), hyperbolic arccosecant acsch(x)
    • rounding functions:
      round down floor(x), round up ceiling(x)
    • the sign of a number:
      sign(x)
    • for probability theory:
      the error function erf(x) (integral of probability), Laplace function laplace(x)
    • Factorial of x:
      x! or factorial(x)
    • Gamma function gamma(x)
    • Lambert's function LambertW(x)
    • Trigonometric integrals: Si(x), Ci(x), Shi(x), Chi(x)

    The insertion rules

    The following operations can be performed

    2*x
    - multiplication
    3/x
    - division
    x^2
    - squaring
    x^3
    - cubing
    x^5
    - raising to the power
    x + 7
    - addition
    x - 6
    - subtraction
    Real numbers
    insert as 7.5, no 7,5

    Constants

    pi
    - number Pi
    e
    - the base of natural logarithm
    i
    - complex number
    oo
    - symbol of infinity
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