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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int 8 x cos^{2} (x) d x

\frac{\partial}{\partial x} ((x - 7)^{2} + (y - 1)^{2} + 29)

x \to 4 lim (\frac{3}{x - 4})

n \to \infty lim (i = 3 \sum 8 (i + 1)^{2})

\int \frac{1}{11 - x ^{2}} d x

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