What is (\partial)/(\partial y)(5xe^{x^2+y^2}) ?

The answer to (\partial)/(\partial y)(5xe^{x^2+y^2}) is 10e^{x^2+y^2}xy

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(\partial)/(\partial y)(5xe^{x^2+y^2})

\frac{\partial}{\partial y} (5 x e^{x^{2} + y^{2}})

10 e^{x^{2} + y^{2}} x y

Solution steps

\frac{\partial}{\partial y} (5 x e^{x^{2} + y^{2}})

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 x \frac{\partial}{\partial y} (e^{x^{2} + y^{2}})

Apply the chain rule:

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

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

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

= 5 x e^{x^{2} + y^{2}} \cdot 2 y

Simplify

= 10 e^{x^{2} + y^{2}} x y

\frac{d}{d x} (\frac{d y}{d x}) = y

\frac{d}{d x} (ln (\frac{K}{x}))

\int e^{- 15 x} d x

\frac{1}{s ^{2} + 7}

\int (n + 3)^{3} d n

What is (\partial)/(\partial y)(5xe^{x^2+y^2}) ?
The answer to (\partial)/(\partial y)(5xe^{x^2+y^2}) is 10e^{x^2+y^2}xy