# How do you find the derivative of the function: #arccos (e^(2x))#?

so:

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To find the derivative of the function arccos(e^(2x)), we can use the chain rule.

Let y = arccos(e^(2x)).

Then, differentiate both sides with respect to x:

dy/dx = d(arccos(e^(2x)))/dx.

Using the chain rule:

dy/dx = -1 / sqrt(1 - (e^(2x))^2) * d(e^(2x))/dx.

Now, find the derivative of e^(2x):

d(e^(2x))/dx = 2e^(2x).

Substitute this back into the equation:

dy/dx = -1 / sqrt(1 - (e^(2x))^2) * 2e^(2x).

Simplify:

dy/dx = -2e^(2x) / sqrt(1 - e^(4x)).

So, the derivative of arccos(e^(2x)) with respect to x is -2e^(2x) / sqrt(1 - e^(4x)).

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