Mercedes

**Solution:**

**Concept:**The derivative of a function is the rate of change of the function or in other words, it is the amount of change in function at a given point. It is denoted by .

The derivative of some functions are given in the table below:

**Calculation:**

**Step:1 **The function is .

Now take the derivative of the above equation.

**Step:2** Simplify further to solve for the derivate as shown below:

**Step:3 **From the Table 1, the derivative of cos*x*is . Use the value of derivative of cos*x* and solve further as below:

The derivative valueis .

**Answer:**The derivative of is .

** **

**Similar Problems:**

**Problem 1:**What is the derivative of ?

**Solution:**

**Step:1 **The function can be written as given below:

**Step:2 **Now take the derivative of the above equation.

**Step:3 **From the above Table 1 shows that the derivative of cos*x*is , therefore solve the derivative further as below:

Since , then the derivative value becomes .

**Answer:**The derivative of is .

** **

**Problem 2:**What is the derivative of ?

**Solution:**

**Step:1 **The function can be written as given below:

**Step:2** Now take the derivative of the above equation.

**Step:3 **From the above Table 1 shows that the derivative of is , therefore solve the derivative further as below:

Since , then the derivative value becomes .

**Answer:** The derivative of is .

** **

** **

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