Question

What is the relationship between the directional derivative, the gradient, partial derivatives and the vector component?

What is the relationship between the directional derivative, the gradient, partial derivatives and the vector component?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Define directional derivatives and the gradient vector in your own words and use material from the...
Define directional derivatives and the gradient vector in your own words and use material from the textbook and lectures as evidence. Please remember to cite your sources if you take information directly from a source. In your own words, describe how gradient vectors could be applied to your future career or how it could be applied in the real-world. Use reputable resources including but note limited to, the textbook and lecture material, to support your answer. In a sentence or...
Let f be a function of two variables that has continuous partial derivatives and consider the...
Let f be a function of two variables that has continuous partial derivatives and consider the points A(8, 6), B(11, 6), C(8, 10), and D(14, 14). The directional derivative of f at A in the direction of the vector AB is 9 and the directional derivative at A in the direction of AC is 8. Find the directional derivative of f at A in the direction of the vector AD. (Round your answer to two decimal places.
Let f be a function of two variables that has continuous partial derivatives and consider the...
Let f be a function of two variables that has continuous partial derivatives and consider the points A(1, 1), B(7, 1), C(1, 13), D(9, 16). The directional derivative of f at A in the direction of the vector AB is 9 and the directional derivative at A in the direction of AC is 2. Find the directional derivative of f at A in the direction of the vector AD. (Round your answer to two decimal places.)
Find the gradient of the function and the max value of the directional derivative at the...
Find the gradient of the function and the max value of the directional derivative at the given point. f(x,y) = y2ex^(-2)y + x3y at the point (1,1)
Find the gradient ∇f and the directional derivative at the point P (1,−1,2) in the direction...
Find the gradient ∇f and the directional derivative at the point P (1,−1,2) in the direction a = (2,−1,1) for the function f (x,y,z) = x^3z − y(x^2) + z^2. In which direction is the directional derivative at P decreasing most rapidly and what is its value?
Use the gradient to find the directional derivative of the function at P in the direction...
Use the gradient to find the directional derivative of the function at P in the direction of PQ. f(x, y) = 3x2 - y2 + 4,    P(7, 7), Q(2, 6)
Use the gradient to find the directional derivative of the function at P in the direction...
Use the gradient to find the directional derivative of the function at P in the direction of PQ. g(x, y, z) = xye2z,    P(5, 10, 0), Q(0, 0, 0)
f(x,y,z) = xey+z. (a) Find the gradient of f, ∇f. (b) Find the directional derivative of...
f(x,y,z) = xey+z. (a) Find the gradient of f, ∇f. (b) Find the directional derivative of f at the point (2, 1, 2) in the direction of ? = 3? + 4?.
For z=x2-xy2 find: a. the gradient of Z b. the directional derivative in direction of <3,1>...
For z=x2-xy2 find: a. the gradient of Z b. the directional derivative in direction of <3,1> c. the approximation for Δ? when taking a Δs =0.05 step from (1,2) in direction of <3,-1> d. the approximation to the maximum Δ? possible when taking a Δs =0.05 step from (1,2).
Explain why the relationship between partial molar volume and mole fraction of a component in a...
Explain why the relationship between partial molar volume and mole fraction of a component in a mixture is not linear.