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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x^{2} + y^{2}}, g = y

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

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

\frac{\partial}{\partial y} (y) = 1

= 2 (e^{x^{2} + y^{2}} \cdot 2 yy + 1 \cdot e^{x^{2} + y^{2}})

Simplify

2 (e^{x^{2} + y^{2}} \cdot 2 yy + 1 \cdot e^{x^{2} + y^{2}}) : 2 (2 e^{x^{2} + y^{2}} y^{2} + e^{x^{2} + y^{2}})

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

\int \frac{x ^{\frac{1}{3}} - 3}{x ^{\frac{2}{3}}} d x

\int_{0}^{2} 1 + 4 x^{2} d x

q^{^{'}} + \frac{q}{20 + t} = 1, q (0) = 5

x^{8} (x - 3)^{7}

n = 0 \sum \infty \frac{5}{4 ^{n + 1}}

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