Mister Exam

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You entered:

xy^2

x*y^2 = 0

(x*y)^2 = 0

x^(y^2) = 0

x^(y^2) = 0

Plot xy^2

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  2    
xy  = 0

$$xy^{2} = 0$$

Find the derivative

(x^2 + y^2)^2 + 18*(x^2 + y^2) = 8*x^3 - 24*y^2*x + 27

(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (3 / 5)^4

(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (4 / 5)^4

(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (6 / 5)^4

(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (7 / 5)^4

(x^2 + y^2)^2 - 2*(x^2 - y^2) + 1 = (8 / 5)^4

2*y^2*(x^2 + y^2) - 10*y^2*(x + y) - 2*y^2 - 9*x^2 + 90*(x + y) - 144 = 0

(y^2 - x^2)*(x - 1)*(2*x - 3) = 4*(x^2 + y^2 - 2*x)

y^2 = x*(81*x^5 + 396*x^4 + 738*x^3 + 660*x^2 + 269*x + 48)

144*(x^4 + y^4) - 225*(x^2 + y^2) + 350*x^2*y^2 + 81 = 0

(x^2 + y^2)^2 + 8*x*(x^2 + y^2) - 16*y^2 = 0

x + sqrt(1 - y^2) = ln([1 + sqrt(1 - y^2)]/y)/2

x + sqrt(1 - y^2) = 3*ln([1 + sqrt(1 - y^2)]/y)/2

x = abs(ln([1 + sqrt(1 - y^2)]/y) - sqrt(1 - y^2))

(2*x^2 + y^2)^2 - 2*sqrt(2)*x*(2*x^2 - 3*y^2) + 2*(y^2 - x^2) = 0

x^3 + x*y^2 - x^2 + y^2 = y*(x^2 + y^2 - 2*x)

-243 - 216*z - 18*x + 4*y^2 + 25*x^2 + 36*z^2 + 16*x*y = 0

x^2+4*y^2+9*z^2+4*x*y+12*y*z+6*x*z-4*x-8*y-12*z+3=0

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 following operations can be performed