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 = ln(5x^2 + 3), find dy/dx at x = 1.
If y = ln(5x^2 + 3), find dy/dx at x = 1.
Expand All
Collapse All
Practice Questions
1 question
Q1
If y = ln(5x^2 + 3), find dy/dx at x = 1.
5/8
3/8
1/8
1/5
Show Solution
Copy
dy/dx = (10x)/(5x^2 + 3). At x = 1, dy/dx = (10)/(5(1) + 3) = 10/8 = 5/4.
Questions & Step-by-step Solutions
1 item
Q
Q: If y = ln(5x^2 + 3), find dy/dx at x = 1.
Solution:
dy/dx = (10x)/(5x^2 + 3). At x = 1, dy/dx = (10)/(5(1) + 3) = 10/8 = 5/4.
Steps: 9
Show Steps
Step 1: Identify the function y = ln(5x^2 + 3).
Step 2: Use the chain rule to find the derivative dy/dx. The derivative of ln(u) is (1/u) * (du/dx), where u = 5x^2 + 3.
Step 3: Calculate du/dx. Since u = 5x^2 + 3, the derivative du/dx = 10x.
Step 4: Substitute u and du/dx into the derivative formula: dy/dx = (1/(5x^2 + 3)) * (10x).
Step 5: Simplify the expression: dy/dx = (10x)/(5x^2 + 3).
Step 6: Now, substitute x = 1 into the derivative: dy/dx = (10(1))/(5(1)^2 + 3).
Step 7: Calculate the denominator: 5(1)^2 + 3 = 5 + 3 = 8.
Step 8: Now, calculate dy/dx at x = 1: dy/dx = 10/8.
Step 9: Simplify 10/8 to get 5/4.
Related Questions
I
If y = (2x + 1)^3, find dy/dx.
Question: If y = (2x + 1)^3, find dy/dx.Options: 6(2x + 1)^23(2x + 1)^22(2x + 1)^212(2x + 1)^2Correc..
I
If y = cos(5x^2), find dy/dx.
Question: If y = cos(5x^2), find dy/dx.Options: -10xsin(5x^2)-5xsin(5x^2)-25xsin(5x^2)-2xsin(5x^2)Co..
I
If y = tan(3x), find dy/dx.
Question: If y = tan(3x), find dy/dx.Options: 3sec^2(3x)3tan^2(3x)sec^2(3x)3tan(3x)Correct Answer: 3..
I
If y = e^(3x), find dy/dx at x = 0.
Question: If y = e^(3x), find dy/dx at x = 0.Options: 13e3eCorrect Answer: 1Solution: dy/dx = 3e^(3x..
I
If y = 4x^3 - 2x + 1, find dy/dx at x = -1.
Question: If y = 4x^3 - 2x + 1, find dy/dx at x = -1.Options: -10-8-6-4Correct Answer: -6Solution: d..
‹
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
✕
↑
