All Categories
Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
General Aptitude
Arithmetic Aptitude
Data Interpretation
Show All General Aptitude
General Knowledge
Basic General Knowledge
General Science
Show All General Knowledge
Medical Science
Anatomy
Biochemical Engineering
Biochemistry
Biotechnology
Microbiology
Show All Medical Science
Technical
Database
Digital Electronics
Electronics
Networking
Show All Technical
Verbal and Reasoning
Logical Reasoning
Verbal Ability
Verbal Reasoning
Show All Verbal and Reasoning
›
If y = tan(3x), find dy/dx at x = π/6.
If y = tan(3x), find dy/dx at x = π/6.
Expand All
Collapse All
Practice Questions
1 question
Q1
If y = tan(3x), find dy/dx at x = π/6.
3√3
3
√3
1
Show Solution
Copy
dy/dx = 3sec^2(3x). At x = π/6, dy/dx = 3sec^2(π/2) = 3(∞) = undefined.
Questions & Step-by-step Solutions
1 item
Q
Q: If y = tan(3x), find dy/dx at x = π/6.
Solution:
dy/dx = 3sec^2(3x). At x = π/6, dy/dx = 3sec^2(π/2) = 3(∞) = undefined.
Steps: 8
Show Steps
Step 1: Identify the function given in the question, which is y = tan(3x).
Step 2: To find dy/dx, we need to use the chain rule of differentiation. The derivative of tan(u) is sec^2(u), where u is a function of x.
Step 3: In our case, u = 3x. Therefore, the derivative dy/dx = d(tan(3x))/dx = sec^2(3x) * d(3x)/dx.
Step 4: The derivative of 3x with respect to x is 3. So, we have dy/dx = 3 * sec^2(3x).
Step 5: Now, we need to evaluate dy/dx at x = π/6. Substitute x = π/6 into the derivative: dy/dx = 3 * sec^2(3 * (π/6)).
Step 6: Simplify the expression: 3 * (π/6) = π/2. So, we need to find sec^2(π/2).
Step 7: The secant function is the reciprocal of the cosine function. Since cos(π/2) = 0, sec(π/2) = 1/0, which is undefined.
Step 8: Therefore, sec^2(π/2) is also undefined. This means dy/dx at x = π/6 is undefined.
Related Questions
I
If y = (x^2 + 1)^5, find dy/dx.
Question: If y = (x^2 + 1)^5, find dy/dx.Options: 10x(x^2 + 1)^45(x^2 + 1)^45x(x^2 + 1)^420x(x^2 + 1..
I
If y = 5x^4 - 3x^3 + 2x - 1, find dy/dx at x = 1.
Question: If y = 5x^4 - 3x^3 + 2x - 1, find dy/dx at x = 1.Options: 14161820Correct Answer: 16Soluti..
I
If y = √(x^2 + 1), find dy/dx at x = 1.
Question: If y = √(x^2 + 1), find dy/dx at x = 1.Options: 1/√21/212Correct Answer: 1/√2Solution: dy/..
I
If y = 4x^2 + 3x + 2, find dy/dx at x = -1.
Question: If y = 4x^2 + 3x + 2, find dy/dx at x = -1.Options: -5-315Correct Answer: -5Solution: dy/d..
I
If y = e^(3x), find dy/dx.
Question: If y = e^(3x), find dy/dx.Options: 3e^(3x)e^(3x)9e^(3x)6e^(3x)Correct Answer: 3e^(3x)Solut..
‹
Biology (School & UG)
Chemistry (School & UG)
Civil Engineering
Commerce & Accountancy
Computer Science & IT
Current Affairs & GK
Data Structures & Algorithms
Electrical & Electronics Engineering
English (School)
General Aptitude
General Knowledge
General Knowledge & Current Affairs
Languages & Literature
Law & Legal Studies
Major Competitive Exams
Mathematics (School)
Mechanical Engineering
Medical Science
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Social Science (School)
Technical
Verbal and Reasoning
Vocational & Skill Development
›
Soulshift Feedback
×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy
?
0
1
2
3
4
5
6
7
8
9
10
Not likely
Very likely
✕
↑
