12. $$ [-/ 1.07 $$ Points $$ ] $$ DETAILS MY NOTES Find the derivative of the function. Simplify if possible. $$ y=\arccos \left(e^{6 x}\right) $$ $$ y^{\prime}=\square $$

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1. Let $$ u = e^{6x} $$, so that the function becomes $$ y = \arccos(u) $$.

2. The derivative of $$ \arccos(u) $$ with respect to $$ u $$ is 
   $$
   \frac{d}{du}\arccos(u) = -\frac{1}{\sqrt{1-u^2}}.
   $$

3. Next, calculate the derivative of $$ u = e^{6x} $$ with respect to $$ x $$:
   $$
   \frac{du}{dx} = 6e^{6x}.
   $$

4. Apply the chain rule:
   $$
   \frac{dy}{dx} = \frac{d}{du}\arccos(u) \cdot \frac{du}{dx} = -\frac{1}{\sqrt{1-u^2}} \cdot 6e^{6x}.
   $$

5. Substitute back $$ u = e^{6x} $$:
   $$
   \frac{dy}{dx} = -\frac{6e^{6x}}{\sqrt{1-(e^{6x})^2}}.
   $$

6. Simplify the expression by writing $$ (e^{6x})^2 $$ as $$ e^{12x} $$:
   $$
   \frac{dy}{dx} = -\frac{6e^{6x}}{\sqrt{1-e^{12x}}}.
   $$

Thus, the derivative of the function is 
$$
y' = -\frac{6e^{6x}}{\sqrt{1-e^{12x}}}.
$$
$$ y' = -\frac{6e^{6x}}{\sqrt{1-e^{12x}}} $$

Points DETAILS MY NOTES
Find the derivative of the function. Simplify if possible.

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Points DETAILS MY NOTES Find the derivative of the function. Simplify if possible.