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?

IIT JAM Question

Asf Institute
2 weeks ago
 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)

This discussion on 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? is done on EduRev Study Group by IIT JAM Students. The Questions and Answers 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? are solved by group of students and teacher of IIT JAM, which is also the largest student community of IIT JAM. If the answer is not available please wait for a while and a community member will probably answer this soon. You can study other questions, MCQs, videos and tests for IIT JAM on EduRev and even discuss your questions like 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? over here on EduRev! Apart from being the largest IIT JAM community, EduRev has the largest solved Question bank for IIT JAM.