# Question #bcf6f

##### 1 Answer

I understand the question is how the derivative of

#### Explanation:

The answer is obtained by applying the properties of the derivation and the rule of the chain. First, since our function is a subtraction between two expressions, its derivative will be the subtraction of the derivatives of both expressions separately:

Now, we must apply the derivative of the logarithm (using the chain rule also), which is:

with which we will have the following:

Finally, we derive the sine and cosine:

The derivative is already calculated. We can leave the result or try to simplify it a little ...

We add the two fractions and use the fundamental theorem of trigonometry to simplify the fraction obtained:

We can improve it a little more, remembering the formula of the sine of the double angle:

Using this formula, the expression of the derivative may be simplified as follows: