
How do you differentiate ?
Answer
479.7k+ views
Hint: Here, we have to find the derivative of the given function. We will differentiate the given function by using the chain rule and by using the derivative formula. Differentiation is a method of finding the derivative of the function and finding the rate of change of a function with respect to one variable.
Formula used:
We will use the following formulas:
Derivative formula:
Derivative formula of Power rule:
Complete Step by Step Solution:
We are given a function .
Now, by differentiating both sides of the given function with respect to , we get
We know that if a function has two functions, then both the functions have to be differentiated separately.
We are given a trigonometric function of the sine of the algebraic function raised to the power 2. First, we will find the derivative of the trigonometric function and then the derivative of the algebraic function.
By using the derivative formula and by using the chain rule, we get
Now using the derivative formula of Power rule , we get
Therefore, the derivative of is .
Note: We have used the chain rule to find the derivative of the composite functions. Chain rule states that if a composite function where and be two functions, then the derivative of the composite function is . If there is an arithmetic operation of addition and subtraction, then it appears as the same, but if no such arithmetic operation exists, then all these functions have to be the product of all the functions.
Formula used:
We will use the following formulas:
Derivative formula:
Derivative formula of Power rule:
Complete Step by Step Solution:
We are given a function
Now, by differentiating both sides of the given function with respect to
We know that if a function has two functions, then both the functions have to be differentiated separately.
We are given a trigonometric function of the sine of the algebraic function raised to the power 2. First, we will find the derivative of the trigonometric function and then the derivative of the algebraic function.
By using the derivative formula
Now using the derivative formula of Power rule
Therefore, the derivative of
Note: We have used the chain rule to find the derivative of the composite functions. Chain rule states that if a composite function
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Trending doubts
Which are the Top 10 Largest Countries of the World?

Why is insulin not administered orally to a diabetic class 12 biology CBSE

a Tabulate the differences in the characteristics of class 12 chemistry CBSE

Why is the cell called the structural and functional class 12 biology CBSE

The total number of isomers considering both the structural class 12 chemistry CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
