IIT JAM Question  >  Let be a twice differentiable function. Defi... Save
Let be a twice differentiable function. Define


f(x,y,z) = g(x2 + y2 - 2z2).



  • a)
    4(x2 + y2 - 4z2) g''(x2 + y2 - 2z2)

  • b)
    4(x2 + y2 + 4z2) g''(x2 + y2 - 2z2)

  • c)
    4(x2 + y2 - 2z2) g''(x2 + y2 - 2z2)

  • d)
    4(x2 + y2 + 4z2) g''(x2 + y2 - 2z2) + 8g′(x2 + y2 − 2z2)

Correct answer is option 'A'. Can you explain this answer?

Related Test

Answers

Asf Institute
Jan 19, 2021
Related Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer?
 Correct Answer :- A
Explanation : f(x,y,z) = g(x2 + y2 - 2z2).
df'/dx = g'(x2 + y2 - 2z2) (2x)
df"/dx” = g"(x2 + y2 - 2z2) (4x2) + g'(x2 + y2 - 2z2)*2.........(1)
df/dy = g'(x2 + y2 - 2z2) (2y)
df"/dy” = g"(x2 + y2 - 2z2) (4y2) + g'(x2 + y2 - 2z2)*2.........(2)
df'/dz = g'(x2 + y2 - 2z2) (2y)
df"/dz” = g"(x2 + y2 - 2z2) (4z2) + g'(x2 + y2 - 2z2)*2.........(3)
Adding (1), (2) and (3)
g"(x2 + y2 - 2z2)(4x2 + 4y2 + 16z2) + g'(x2+ y2 - 2z2) (2 + 2 - 4)
= 4(x2 + y2 + 4z2) g"(x2 + y2 - 2z2)

View courses related to this question
Explore IIT JAM courses
Explore IIT JAM courses
View courses related to this question
1 Crore+ students have signed up on EduRev. Have you?
Question Description
Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2022 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2022 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer?.
Solutions for Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free.
Here you can find the meaning of Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 - 2z2).a)4(x2 + y2 - 4z2) g(x2 + y2 - 2z2)b)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)c)4(x2 + y2 - 2z2) g(x2 + y2 - 2z2)d)4(x2 + y2 + 4z2) g(x2 + y2 - 2z2)+ 8g′(x2 + y2 − 2z2)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice IIT JAM tests.
Correct Answer :- AExplanation : f(x,y,z) = g(x2 + y2 - 2z2).df/dx = g(x2 + y2 - 2z2) (2x)df"/dx” = g"(x2 + y2 - 2z2) (4x2) + g(x2 + y2 - 2z2)*2.........(1)df/dy = g(x2 + y2 - 2z2) (2y)df"/dy” = g"(x2 + y2 - 2z2) (4y2) + g(x2 + y2 - 2z2)*2.........(2)df/dz = g(x2 + y2 - 2z2) (2y)df"/dz” = g"(x2 + y2 - 2z2) (4z2) + g(x2 + y2 - 2z2)*2.........(3)Adding (1), (2) and (3)g"(x2 + y2 - 2z2)(4x2 + 4y2 + 16z2) + g(x2+ y2 - 2z2) (2 + 2 - 4)= 4(x2 + y2 + 4z2) g"(x2 + y2 - 2z2)