
How do you find the derivative of ?
Answer
484.2k+ views
Hint: We know that tangent is the ratio of sine and cosine function. That is . To solve this we use the quotient rule that, if the two functions and are differentiable then the quotient is differentiable and .
Complete step-by-step answer:
Given, .
We need to find the differentiation of .
We know from the definition of tangent we have .
So we have,
.
Now differentiating with respect to ‘x’, we have
We know that and are differentiable. Now we have quotient rule . Where and .
So we have,
.
We know and , substituting we have,
We know the product of two negative number will give us the positive number, we have
.
Taking 2 common the numerator we have,
.
We know the Pythagoras trigonometric identity. That Is .
We know that the reciprocal of cosine is secant, we get
.
Thus we have .
So, the correct answer is “ ”.
Note: We have different types of differentiation rules.
Sum or difference rule: when the function is the sum or difference of two functions, the derivative is the sum or difference of derivative of each function. i.e.,
then .
Product rule: when f(x) is the product of two function that is then . We use this rule depending on the given problem.
In the problem of differentiation involving trigonometric function, to simplify further we need to know all the trigonometric identities. We know the reciprocal of sine, cosine and tangent are cosecant, secant and cotangent respectively.
Complete step-by-step answer:
Given,
We need to find the differentiation of
We know from the definition of tangent we have
So we have,
Now differentiating with respect to ‘x’, we have
We know that
So we have,
We know
We know the product of two negative number will give us the positive number, we have
Taking 2 common the numerator we have,
We know the Pythagoras trigonometric identity. That Is
We know that the reciprocal of cosine is secant, we get
Thus we have
So, the correct answer is “
Note: We have different types of differentiation rules.
Sum or difference rule: when the function is the sum or difference of two functions, the derivative is the sum or difference of derivative of each function. i.e.,
Product rule: when f(x) is the product of two function that is
In the problem of differentiation involving trigonometric function, to simplify further we need to know all the trigonometric identities. We know the reciprocal of sine, cosine and tangent are cosecant, secant and cotangent respectively.
Recently Updated Pages
Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
Which one of the following is a true fish A Jellyfish class 12 biology CBSE

Which are the Top 10 Largest Countries of the World?

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

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Derive an expression for electric potential at point class 12 physics CBSE
