
What is the derivative of ?
Answer
413.7k+ views
Hint: We use Product – Rule to find the derivative of function .
The product rule helps us to differentiate between two or more of the functions in a given function.
If and are the two given function of then the product rule is given by the following formula:
. After product rule we use different trigonometric identities such as and to solve the given problem.
Complete step by step answer:
The given function is the product of two functions and .
We use product rule to find the derivative, that means first we multiply the first function by the derivative of the second function and the second function is multiplied by the derivative of the first function and add them.
So, we can write it as
We know that the derivative of and the derivative of .
So, and
Put these values in equation . We get,
Simplifying the above equation. We get,
We know that and .
Write these values in the above equation. We get,
Hence, the derivative of the function is .
Note:
To find the derivative of the given function we can also use chain rule. First we simplify the expression by opening brackets and we will get a composite function. Chain rule is used where the function is composite, we can denote chain rule by , where and are two functions. Chain rule states that the derivative of a composite function can be taken as the derivative of the outer function which we multiply by the derivative of the inner function.
The product rule helps us to differentiate between two or more of the functions in a given function.
If
Complete step by step answer:
The given function is the product of two functions
We use product rule to find the derivative, that means first we multiply the first function by the derivative of the second function and the second function is multiplied by the derivative of the first function and add them.
So, we can write it as
We know that the derivative of
So,
Put these values in equation
Simplifying the above equation. We get,
We know that
Write these values in the above equation. We get,
Hence, the derivative of the function
Note:
To find the derivative of the given function we can also use chain rule. First we simplify the expression by opening brackets and we will get a composite function. Chain rule is used where the function is composite, we can denote chain rule by
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