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

The answer to (\partial)/(\partial x)(2e^{x^3y}) is 6e^{x^3y}x^2y

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(\partial)/(\partial x)(2e^{x^3y})

\frac{\partial}{\partial x} (2 e^{x^{3} y})

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

Solution steps

\frac{\partial}{\partial x} (2 e^{x^{3} y})

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (e^{x^{3} y})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x^{3} y) = 3 y x^{2}

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

Simplify

= 6 e^{x^{3} y} x^{2} y

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What is (\partial)/(\partial x)(2e^{x^3y}) ?
The answer to (\partial)/(\partial x)(2e^{x^3y}) is 6e^{x^3y}x^2y