Find the directional derivative of f=xyz at (1,1,1) in the direction of 𝑖⃗ +𝑗⃗ +𝑘⃗
Question
Solution 1
To find the directional derivative of f=xyz at (1,1,1) in the direction of 𝑖⃗ +𝑗⃗ +𝑘⃗, we can use the formula:
Df = ∇f · 𝑢
where ∇f is the gradient of f and 𝑢 is the unit vector in the direction of 𝑖⃗ +𝑗⃗ +𝑘⃗.
Step 1: Calculate the gradient of f The gradient of f is given by:
∇f = (∂f/∂x, ∂f/∂y, Knowee AI is a powerful AI-powered study tool designed to help you to solve study prob
, ∂f/∂y, Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem. Kno
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