# How do you find the derivative of  ?

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 cosxis  . Use the value of derivative of cosx and solve further as below:

The derivative valueis  .

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 cosxis  , therefore solve the derivative further as below:

Since  , then the derivative value becomes  .

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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