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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?
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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
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
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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?.
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?.
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