Topic: Electronics Engineering
Directional derivative of $U=2x^{3}y-3y^{2}z$ at $P(1,2,-1)$ in a direction towards $Q(3,-1,5)$ is
- A. -90/7
- B. 30/7
- C. 90/49
- D. None of these
Answer: D. None of these
Explanation: $\nabla U=6x^{2}y~a_{x}+(2x^{3}-6yz)a_{y}-3y^{2}a_{z}$. At $P(1,2,-1)$, $\nabla U=12a_{x}+14~a_{y}-12~a_{z}$. Directional derivative $\frac{dU}{dl}=\nabla U\cdot a_{1} = (12,14,-12)\cdot\frac{(3,-1,5)}{\sqrt{35}} = \frac{12\times3-14\times1-12\times5}{\sqrt{35}} = \frac{-38}{\sqrt{35}}$.