
What is the derivative of ?
Answer
453k+ views
Hint: In this question we have been asked to find the derivative of the given trigonometric function . We will first rewrite the expression in the form of and then we will use the formula of the derivative of the term in the form of . We will use the formula and simplify the terms to get the required solution.
Complete step-by-step solution:
We have the term given to us as:
Since we have to find the derivative of the term, it can be written as:
Now we know that therefore, on substituting, we get:
We can see that the expression is in the form of the derivative of .
On using the formula on the expression, we get:
Now we know that , where is any constant value and therefore on substituting them in the expression, we get:
On simplifying the terms, we get:
Now the denominator can be split up and written as:
Now we know that , therefore on substituting, we get:
Now we know that therefore, on substituting, we get:
, which is the required derivative.
Therefore, we can write:
Note: It is to be remembered that the function we used to solve the expression is called as the quotient rule. There also exists another rule which is known as the product rule which deals with expressions in the form of and has formula . It is to be noted that the terms and are also written as and in some solutions.
Complete step-by-step solution:
We have the term given to us as:
Since we have to find the derivative of the term, it can be written as:
Now we know that
We can see that the expression is in the form of the derivative of
On using the formula
Now we know that
On simplifying the terms, we get:
Now the denominator can be split up and written as:
Now we know that
Now we know that
Therefore, we can write:
Note: It is to be remembered that the function we used to solve the expression is called as the quotient rule. There also exists another rule which is known as the product rule which deals with expressions in the form of
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