Question

y = log\sqrt{\frac{1+cos3x}{1+cos3x}}

Answer 1

0

Answer 2

Solution:

We are given

$$y=\log\sqrt{\frac{1+\cos3x}{1+\cos3x}}.$$

Since the numerator and denominator are identical,

$$\frac{1+\cos3x}{1+\cos3x} = 1.$$

Thus,

$$\sqrt{1} = 1 \quad \text{and} \quad y=\log(1)=0.$$

Since $y$ is a constant, its derivative is

$$\frac{dy}{dx}=0.$$

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Explanation (minimal):

Simplify $y$ to get $y=\log1=0$. Therefore, $\frac{dy}{dx}=0$.