Question

63. Find the directional derivative ofP = 4e^2x-y+zat the point (1,1,-1) in aadirection towand the point (-3,5,6)​

Answer 1

Step-by-step explanation:

$p = 4 {e}^{2x} - y + z \: \\ grad \: p =(i \frac{\delta}{ \delta \: x} + j \frac{\delta }{ \delta \: y } + k \frac{\delta}{\delta z} \:)(4 {e}^{2x} - y + z) \\ = 4 {e}^{2x} .2 i- j + k \\ = 8 {e}^{2x} i - j + k \\ at \: (1 \ \: \: 1 \: - 1) \\ gradp =( 8 {e}^{2} i - j + k)$

$direction = a \: vector = - 3i + 5j + 6k$

$directional \: derivative = gradp. \frac{a \: vector}{ |a| } = (8 {e}^{2}i - j + k) \frac{( - 3i + 5j + 6k)}{( \sqrt{ { (- 3)}^{2} + {5}^{2} + {6}^{2} } )} \\ = \frac{ - 24 {e}^{2} - 5 + 6}{9 + 25 + 36} = \frac{ - 24 {e}^{2} + 1 }{60}$

Answer 2

Answer:

Step-by-step explanation: