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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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

\int \frac{x - 4}{x} d x

x, x^{2} - 2, - 1, 4

x \to 4 lim (x + 2)

2 y \cdot sin (x) d x = cos (x) d y - 2 d x

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