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

The answer to (\partial)/(\partial y)(e^{6xy}*6x) is 36e^{6xy}x^2

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (6 x y) = 6 x

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

Simplify

6 x e^{6 x y} \cdot 6 x : 36 e^{6 x y} x^{2}

= 36 e^{6 x y} x^{2}

x \to 0 lim (\frac{8}{x} - \frac{8}{x ^{2} + x})

\int x^{2} - 6 xx d x

\frac{d y}{d x} = 14 x + y - 14

\frac{d}{d x} (x^{2} + y^{2} - 6 x - 4 y - 21)

What is (\partial)/(\partial y)(e^{6xy}*6x) ?
The answer to (\partial)/(\partial y)(e^{6xy}*6x) is 36e^{6xy}x^2