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

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

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(\partial)/(\partial y)(xe^{x^3y})

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\frac{\partial}{\partial x} (\frac{- 2 x - y}{( x - y ) ^{4}})

\int x \cdot ln (\frac{1}{x}) d x

\int \frac{1 - e ^{- 4 x}}{1 + e ^{- 4 x}} d x

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

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