# What is the equation of the tangent line of #f(x) =sqrt(ln(tanx))# at # x = pi/4#?

Find the point

The point is

Next, find the derivative. Let

Then

The chain rule states that

Accordingly:

The slope of the tangent is given by evaluating

The tangent will be a vertical line, with equation

The equation is therefore

Here is a graphical depiction. The function is displayed in

Hopefully this helps!

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The equation of the tangent line of f(x) = sqrt(ln(tanx)) at x = pi/4 is y = (1/2) + sqrt(2).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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