What is (\partial)/(\partial x)(2x^2ye^x+2) ?

The answer to (\partial)/(\partial x)(2x^2ye^x+2) is 2y(e^xx^2+2e^xx)

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(\partial)/(\partial x)(2x^2ye^x+2)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{1}{5 x ^{2} + 20 x - 10} d x

x \to \frac{π}{3} lim (\frac{1}{sec ( x )})

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

\int_{0}^{1} sin^{2} (π x) d x

What is (\partial)/(\partial x)(2x^2ye^x+2) ?
The answer to (\partial)/(\partial x)(2x^2ye^x+2) is 2y(e^xx^2+2e^xx)