Q1: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i b) If W =F(x,y) , where x =r cos 0 and y =r sin e. Find W +W %3!

Q: In Exercises priate variable. 21. y = cos (r) 23. y = sin-'V21 25. y = sec (2s + 1) find the…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 1. The temperature at the point (r, y) on an unevenly heated plate is given by T = f(r, y) = 100+…

A: Given f=100+5x2+15x+10y2gradient of f∇f=∂f∂xi+∂f∂yj     =10x+15i+20yjAt (2, 1)∇f=10x+15i+20yj…

Q: Use the Chain Rule to find the derivative of w = xy with respect to t along the path x = cos t, y =…

A:

Q: In what direction does g have the maximum directional derivative at (x, y) = (4, 1)? What is the %3D…

A: We have to find maximum directional derivative.

Q: Find the directional derivative of f(z, y) = In(e"- 3y) at the point (0, 0) %3D in the direction of…

A: Topic- Direction derivatives of function using partial differentiation .

Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: 6.) Find the directional derivative of g(x,y)=Vx² +y² at the point P(3,4) in the direction of v…

A:

Q: A particle moves in a straight line with the velocity function v(t) = sin(wt)cos*(wt). Find its…

A:

Q: Find the directional derivative of f(x, y) = In(e"- 3y) at the point (0,0) in the direction of 3i +…

A: We are asked to find directional derivatives of function.

Q: 1 Find the direction derivative of f(x, y, z) = x²y -zx -y³x at the point (1,-1,1) in the direction…

A: Directional derivative

Q: Find the directional derivative of the function f(x,y,z) = tan (xýz) At point (1,2,3) İin the…

A: The solution is given as

Q: b) Find the directional derivative (D.) of the function at P in the direction of PQ f(z, y) = sin 2z…

A:

Q: A line passes through the point Po(xo, Yo) and has gradient m = tan a. Show that a general point of…

A: Gradient, or slope of a line characterizes the direction of the line and is found out by dividing…

Q: The directional derivative of f(, y) = In(x² + y²) at the point P(1,5) in the direction v (3, 4) is…

A: We have to find the directional derivative of the function fx, y=lnx2+y2 at the point 1, 5 in the…

Q: Find the directional derivative of k(r, y) = 3edr sin(y) at the point (0, ) in the directi

A:

Q: Consider the function g(x, y) = 2e* sin y a) Prove that there are no critical points of g. b) What…

A:

Q: Consider h(x, y, z) = cos (xy) + eyz + ln (xz). Determine the directional derivative of h at the…

A:

Q: 1. Consider the function g(x, y) = cos(xy) + sin(x – 2y) (a) Determine g (c) Determine (c) What is…

A: Given function is  g(x,y)=cos(xy)+sin(x-2y) we have to find the second order partial derivatives…

Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1, 1) in the direction of from…

A:

Q: 1. Let f(x, y) = x cos(2x + y). a) Find the value of the directional derivative of /(x, y) at| in…

A:

Q: Q1: Find the derivative of f(x,y,z)=x^3-xy^2-2z at point P_o (1,1,0) in the direction of vector…

A: Solution:-

Q: 1. Let f(x, y) = x cos(2x+ y). a) Find the value of the directional derivative of f(x, y) at in the…

A:

Q: What is the directional derivative of the function f(x,y) = 2xy- 3y2 at point po= (5,5) in the…

A: Givenf(x,y)=2xy-3y2 ; p0=(5,5) ; u=4i+3jWe need to find directional derivative Duf(5,5)where…

Q: 2. Find the directional derivative of f(x, y) = -2e* cos y at %3D (0, ) in the direction of v = (-6,…

A:

Q: A line passes through the point P0(x0, y0) and has gradient m = tan α. Show that a general point of…

A:

Q: The directional derivative of 2e" cos y at f(x, y) = -2e* cos y at (0, 7) in the direction of v =…

A:

Q: Section 11.6: Calculus of Vector-Valued Functions - #39

A:

Q: Find the directional derivative of f(x, y) = In(e- 2y) at the point (0, 0) in the direction of 3i +…

A:

Q: a) If W = F(x ,y),where x =v²-g and y 2vg calculate W +W, %3D b) What is the directional derivative…

A: W=f(x,y) and x= v2-g2 & y=2vg   Wx = dW/dx = (df/dx*dx/dv) + (df/dx*dx/dg) ..............From…

Q: 3x The directional derivative of f(x,y,z) = ln (주)을 1+yz from P to Q(-1,-1,2) is given by...…

A: We can solve this using given information

Q: 3x The directional derivative of f(x,y,z)=ln at the point P (2,0,-1) in the direction 1+yz z² from P…

A:

Q: Given a function (r, y, 2) = 3x2 + In (3y2+ 1) + e cos 2. i. Find the directional derivative of o at…

A: Here we will find out the required value.

Q: The directional derivative of f(x, y) = e" cos Y at (0, ) in the direction of v = (-6, 8) is

A:

Q: Find the directional derivative of f(z, y) = In(e" - 3y) at the point (0,0) in the direction of 3i +…

A:

Q: 1. Find the value of the directional derivative at the particular point Po for the given function in…

A: Given that gx,y=y2tan2x ; U→=-32 i^+12 j^ ; P0π3,2We need to find the value of the dorectional…

Q: 8y If the directional derivative of f(x,y)D at (2,1) in the direction of (a, 2) is equal to zero,…

A: Given,            f(x,y)=8yx

Q: Find the directional derivative of f(x, y) = In(e" - 2y) at the point (0,0) %3D in the direction of…

A: take the partial derivative with respect to x put the point (0,0)

Q: If f(x, y, 2) = cos(x - y)+e² , compute directional derivative of f at (5, 5, 0) in the direction of…

A:

Q: Find the directional derivative of f(x,y) v = 3i – 4j. x² sin 2y at (1, 7/2) in the direction of |

A:

Q: 2. Find the directional derivative of f(x, y, z) = y – Væ² + z² at P(-3,1,4) in the direction of a =…

A: Given f(x,y,z)=y-x2+z2

Q: 1. Find the directional derivative of f(x,y) = y²e²" at (0, 1) in the direction of v =.

A:

Q: Use the definition of directional derivative to solve Duf(xo, yo, zo) at point P(xo, yozo) where…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the directional derivative of f(r, y, z) = e cos(ryz) at (0,1,) in 2 - 1 I- 2 the directions…

A: We have to find the directional derivative of f(x,y,z) at 0,1,12 in the directions parallel to the…

Q: Let f(x, y) = -4x + 3y. Find the directional derivative in the direction of v = from the point P =…

A:

Q: The directional derivative of f(x, y) = e" cos y at (0, ) in the direction of v = (-6,8) is

A:

Q: If (x, y, z) = cos(x – y)+ e² compute directional derivative of Í at (3, 3, 0) in the direction of ŷ…

A: Option C is correct option.

Q: Show that r = (sin t)i + (cos t)j + V3k has a constant length. And r(t) is orthogonal to it's…

A: Note: We are supposed to answer only one question. Kindly repost other questions as to the next…

Q: 1. Find the directional derivative of the function f(x, y, z) = 3e" sin(ry) in the direction of v =…

A:

Q: The directional derivative of f(r, y) =-e" cos y at (0, 5) in the direction of v = (-6, 8) is

A: Given that fx,y=-excos y at0,π4and v=-6,8

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.