Consider the function g(x, y) = x² + xy + y² (1 + 1/2t, 2 + V3/2t), use the (a) Given the line l(t) chain rule to compute (g o l)’(0). (b) Compute the derivative of g(x, y) in the (1/2, V3/2) direction at the point (1, 2).

Q: Find the direction derivative of f(x.y.z)-xy'z at the point p(3,2,1)in the direction towards…

A: To find the directional derivatives

Q: Determine the directional derivative of f(x, y) = 3x² + [y] at the point P(-1, -1) along the…

A: Explanation of the answer is as follows

Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

A:

Q: a) Find the directional derivative of the function f(x, y, z)= x² y2 (2z+1)2 at the point P:(1, - 1,…

A:

Q: d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax) then,…

A:

Q: Calculate the directional derivative of y = xz + y? in the direction of 20 – ŷ + 32 at the point (2,…

A: Given that ψ=xz+y2and the direction vector2x⏞ -y⏞+3z⏞The point p0=(2,0,-1) To find the directional…

Q: Find the directional derivative of f (x, y) = -3 yx³ + xy² set by the line r(t)=(-2+ 2t,√5t). at the…

A:

Q: nd the directional derivative of the function f(x,y)=2x²y²+3xy at the point P=(2,-3) in the…

A:

Q: Let f(x) = e»in(²)+z² _ i) Find the x-values of the stationary points to the curve y = f(x), where 0…

A: The given function is  fx=esinx2+x2

Q: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax) then,…

A: The truncation error is of order O∆x3 The step length are ∆x, -∆x

Q: a) Find the derivative of f(x, y, z) = 4zx – xy² – z,at P,(1,0, 2) in the direction of v = 4i – 5j +…

A: Given: The function, fx, y, z=4zx3-xy2-z at P01,0,2 in the direction of v=4i-5j+40k.

Q: (b) Consider the function f(x) = x - 1. Find the average rate of change from 1 to 3, then find the…

A: The average rate of change of a function is defined by the formula . This average rate is also…

Q: Find f '(2), where f(t) = u(t) v(t), ū(2) = (1, 2, -1), u' (2) = (3,0, 4), and v(t) = (t, t², t³).

A: