7. Find the gradient for the function ๐ข = ๐(๐), ๐ = โ๐ฅ2 + ๐ฆ2 + ๐ง2.Answer: ๐๐ข = ๐โฒ(๐) ๐๐ .
Question
Solution 1
To find the gradient of the function u = ฯ(r), where r = โ(xยฒ + yยฒ + zยฒ), we need to use the chain rule for differentiation.
Step 1: Differentiate ฯ(r) with respect to r to get ฯโฒ(r).
Step 2: Differentiate r with respect to x, y, and z to get the vector (x/r, y/r, z/r). This is the unit vector in Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv
Similar Questions
7. Find the gradient for the function ๐ข = ๐(๐), ๐ = โ๐ฅ2 + ๐ฆ2 + ๐ง2.Answer: ๐๐ข = ๐โฒ(๐) ๐๐ .
Classify the following partial differential equations:(i) ๐2๐ข๐๐ฅ2 + 3 ๐2๐ข๐๐ฆ2 = ๐๐ข
If ๐ข = ๐ฅ2 tanโ1 ๐ฆ๐ฅ โ ๐ฆ2 tanโ1 ๐ฅ๐ฆ show that ๐2๐ข๐๐ฅ๐๐ฆ = ๐ฅ2โ๐ฆ2๐ฅ2+๐ฆ2 and ๐2๐ข๐๐ฅ๐๐ฆ = ๐2๐ข๐๐ฆ๐๐ฅ.
If ๐ฃ = ๐๐, where ๐2 = ๐ฅ2 + ๐ฆ2 + ๐ง2, then prove that ๐ฃ๐ฅ๐ฅ + ๐ฃ๐ฆ๐ฆ + ๐ฃ๐ง๐ง = ๐(๐ + 1)๐๐โ2.
Find the area of the region above the x-axis, included between the parabola ๐ฆ2=๐๐ฅ and the circle ๐ฅ2+๐ฆ2=2๐๐ฅ.