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

The answer to (\partial)/(\partial x)(3e^{x^3y^3}) is 9e^{x^3y^3}x^2y^3

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= 9 e^{x^{3} y^{3}} x^{2} y^{3}

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What is (\partial)/(\partial x)(3e^{x^3y^3}) ?
The answer to (\partial)/(\partial x)(3e^{x^3y^3}) is 9e^{x^3y^3}x^2y^3