What is (\partial)/(\partial x)(y^2+2e^{x^2}xy) ?

The answer to (\partial)/(\partial x)(y^2+2e^{x^2}xy) is 2y(2e^{x^2}x^2+e^{x^2})

(\partial)/(\partial x)(y^2+2e^{x^2}xy)

\frac{\partial}{\partial x} (y^{2} + 2 e^{x^{2}} x y)

2 y (2 e^{x^{2}} x^{2} + e^{x^{2}})

Solution steps

\frac{\partial}{\partial x} (y^{2} + 2 e^{x^{2}} x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (2 e^{x^{2}} x y)

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (2 e^{x^{2}} x y) = 2 y (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 0 + 2 y (2 e^{x^{2}} x^{2} + e^{x^{2}})

Simplify

= 2 y (2 e^{x^{2}} x^{2} + e^{x^{2}})

\int \frac{ln ( x ^{2} )}{2} d x

t a y l or x^{3} + 8 x - 1, - 1

\frac{\partial}{\partial y} (29 - x^{2} - 4 y^{2})

\frac{d}{d x} (4^{x} lo g_{4} (x))

d er i v a t i v e F (x) = e^{x^{2}}

What is (\partial)/(\partial x)(y^2+2e^{x^2}xy) ?
The answer to (\partial)/(\partial x)(y^2+2e^{x^2}xy) is 2y(2e^{x^2}x^2+e^{x^2})