Let be a twice differentiable function. Defi...
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?

### 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)

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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? 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?.
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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)