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

The answer to (\partial)/(\partial y)(2x^2e^{xy}) is 2e^{xy}x^3

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

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

2 e^{x y} x^{3}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 x^{2} e^{x y} x : 2 e^{x y} x^{3}

= 2 e^{x y} x^{3}

\frac{( s - 2 ) ^{2}}{s ^{3}}

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

\int \frac{1}{( x ^{2} + 4 x + 13 ) ^{3}} d x

\int (4 sin (x) + \frac{2 x ^{5} - x}{x}) d x

f (x) = \frac{4 x ^{\frac{3}{2}}}{x}

What is (\partial)/(\partial y)(2x^2e^{xy}) ?
The answer to (\partial)/(\partial y)(2x^2e^{xy}) is 2e^{xy}x^3