Class 11 Exam  >  Class 11 Questions  >  If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2i... Start Learning for Free
If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2?
Most Upvoted Answer
If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:...
To find the ratio of (dy/dx)^2 to d^2y/dx^2, we need to find the derivatives of y=x^3 with respect to x.

Derivative of y=x^3:
To find the derivative of y=x^3, we can use the power rule:

dy/dx = 3x^(3-1) = 3x^2

Second derivative of y=x^3:
To find the second derivative, we differentiate dy/dx with respect to x:

d^2y/dx^2 = d/dx(3x^2) = 2(3)x^(2-1) = 6x

Ratio of (dy/dx)^2 to d^2y/dx^2:
Now, we can find the ratio of (dy/dx)^2 to d^2y/dx^2 by dividing (dy/dx)^2 by d^2y/dx^2:

(dy/dx)^2 / d^2y/dx^2 = (3x^2)^2 / 6x = 9x^4 / 6x = (9/6)x^4 / x = (3/2)x^3

Therefore, the ratio of (dy/dx)^2 to d^2y/dx^2 is (3/2)x^3.

Answer: C) 3x^3:2
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
Explore Courses for Class 11 exam

Top Courses for Class 11

If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2?
Question Description
If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2?.
Solutions for If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2? in English & in Hindi are available as part of our courses for Class 11. Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2? defined & explained in the simplest way possible. Besides giving the explanation of If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2?, a detailed solution for If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2? has been provided alongside types of If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2? theory, EduRev gives you an ample number of questions to practice If y=x^3 then ratio of (dy/dx)^2 to d^y/dx^2is A)3x:2 B)3x^2:2 C)3x^3:2 D)3x^4:2? tests, examples and also practice Class 11 tests.
Explore Courses for Class 11 exam

Top Courses for Class 11

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev