Discussion
For \( f(x,y) = x^{3} y^{2} \), the partial derivative \( f_{x} \) is
Answer: A
Differentiating with respect to \( x \) treats \( y \) as a constant, so the factor \( y^{2} \) comes along unchanged:
\[ f_{x} \;=\; \frac{\partial}{\partial x}\left(x^{3} y^{2}\right) \;=\; 3x^{2} y^{2}. \]
The form \( 2x^{3}y \) is \( f_{y} \) instead, and \( 6x^{2}y \) is the mixed derivative \( f_{xy} \), got by differentiating once with respect to each variable
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development