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

The answer to (\partial)/(\partial x)(6e^{x^3y}) is 18e^{x^3y}x^2y

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(\partial)/(\partial x)(6e^{x^3y})

\frac{\partial}{\partial x} (6 e^{x^{3} y})

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

Solution steps

\frac{\partial}{\partial x} (6 e^{x^{3} y})

Treat

y

as a constant

Take the constant out:

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

= 6 \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}

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

Simplify

= 18 e^{x^{3} y} x^{2} y

t an g e n t f (x) = 3 x^{3} - x^{2} + 8, (2, 28)

\frac{d}{d x} (8 - x^{2})

d er i v a t i v e y = (t)^{t}

x \to \frac{1}{3} lim (\frac{x + 3}{x + 4})

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

What is (\partial)/(\partial x)(6e^{x^3y}) ?
The answer to (\partial)/(\partial x)(6e^{x^3y}) is 18e^{x^3y}x^2y