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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?
Verified Answer
Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 -...
 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)
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Most Upvoted Answer
Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 -...
 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)
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Community Answer
Let be a twice differentiable function. Define f(x,y,z) = g(x2 + y2 -...
 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)
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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 2025 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 2025 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?.
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