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

The answer to (\partial)/(\partial x)(y^3e^{xy}) is e^{yx}y^4

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(\partial)/(\partial x)(y^3e^{xy})

\frac{\partial}{\partial x} (y^{3} e^{x y})

e^{y x} y^{4}

Solution steps

\frac{\partial}{\partial x} (y^{3} e^{x y})

Treat

y

as a constant

Take the constant out:

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

= y^{3} \frac{\partial}{\partial x} (e^{x y})

Apply the chain rule:

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

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

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

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

Simplify

y^{3} e^{x y} y : e^{y x} y^{4}

= e^{y x} y^{4}

f (x) = 8 x

\frac{\partial}{\partial x} (\frac{8 x}{y})

4 e^{2 t}

\int (x^{4}) d x

\frac{d}{d t} (5)

What is (\partial)/(\partial x)(y^3e^{xy}) ?
The answer to (\partial)/(\partial x)(y^3e^{xy}) is e^{yx}y^4