y^2esqrt(x^2+y^2) derivative

Derivative

d/dx(y^2 e sqrt(x^2 + y^2)) = (e x y^2)/sqrt(x^2 + y^2)

Contour plot

Contour plot

Real roots

x<0, y = 0
x = 0, y<0
x = 0, y>0
x>0, y = 0

Properties as a function

Domain

{(x, y) element R^2 : x^2 + y^2>0}

Range

R (all real numbers)

Parity

odd

Root for the variable y

y = 0

Series expansion at x=0

e x sqrt(y^2) - (e x^3)/(2 sqrt(y^2)) + (3 e x^5)/(8 (y^2)^(3/2)) - (5 x^7 (e sqrt(y^2)))/(16 y^6) + O(x^9) (Taylor series)
Big‐O notation »

Series expansion at x=∞

e y^2 - (e y^4)/(2 x^2) + O((1/x)^4) (Laurent series)
Big‐O notation »

Indefinite integral

integral(e x y^2)/sqrt(x^2 + y^2) dx = e y^2 sqrt(x^2 + y^2) + constant

Limit

lim_(x->-∞) (e x y^2)/sqrt(x^2 + y^2) = -e y^2≈-2.71828 y^2
lim_(x->∞) (e x y^2)/sqrt(x^2 + y^2) = e y^2≈2.71828 y^2
POWERED BY THE WOLFRAM LANGUAGE