Find Duf at (2,−1,1) for f(x, y, z) = 3x5y²z³ in the direction given by u = (1/3, 2/3, −2/3).

Q: If f(x, y) = x cosy + ye*, find a2f дхду

A: Partial derivative: A partial derivative of a function is defined as the derivative of the function…

Q: Given f(x, y) = x³y + 7xy². Compute: 8²f 8x² 8²f by²

A:

Q: Find a direction in the xy-plane in which f(x, y) = e¹-xy has zero change at the point P(1.0. e).

A: We know directional derivative formula Du→fa, b, c=∇fa, b, c.u^ Lets say u→=cosθ, sinθ be the…

Q: f(r, y) : = V3x? + 4y? fz(3, – 2) =|

A:

Q: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

A:

Q: f(x,y) = 40x+ + 72x³y+ 85XU fur eblidl w jall dissui %3D -226x2 A O -226 BO 216x2 CO

A: To find fyx = ?   Given : f(x,y) = 40x4 + 72x3y + 85x

Q: Find dy 3 2. -3x

A: Given that, f(x)=x3-3x We have to find derivative of the given function.

Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: Evaluate: d dxJ (21² + 5)² dt.

A:

Q: Solve: (x+y)dy-(x - y)dx=0 A. x² - 2xy-y²= B. x² + 2xy + y² =c C. x² + y² =c D. x² - 2xy + y² =

A: The given equation is(x+y)dy-(x-y)dx=0 To solve the differential equation.

Q: Evaluate (2x - y) dx + (x + 7y) dy. C C: x-axis from x = 0 to x = 2

A:

Q: Evaluate the value of I = f(e6 − 3x)dx + (6xeº + y)dy, r where I is the straight line from (0, 0) to…

A: On the curve Gamma , which is straight line from (0, 0) to (3,0) we have, y=0 and x  ranges from 0…

Q: Consider (x, y, z) = 4xy²+ 3y sin(z) and at the point P = (1,2,0) calculate the directions in which…

A: Approach to solving the question:To find the directions in which the…

Q: Eliminate the constant: =c₁e²x+c₂e³ 3x

A:

Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

A:

Q: let r (t) = The y component of r' (5)

A:

Q: The temperature at the point (x, y) on a metal plate is given by T (x, y) = y/(x2 + y2 ). Find the…

A:

Q: 5. Find the linear approximation of f (x, y, z) = x³y² + 22 at the point (2, 3,4). Use this to…

A:

Q: xa, ya, + za Let A = (x² + y? + )3/2 i show that V X A = 0.

A:

Q: 2. Integrate: S w5 V7+ w3 dw 3. Find S (6-+ - sV) de

A:

Q: f(x,y) = eY Then: 12zy fxxyz2= x2 2zy 13 12z y2 fxxy 1223y2

A:

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

A:

Q: Find Joy²dx + (xy-x²) dy along C: y = 7x from (0,0) to (1, 7).

A:

Q: ſx = s² – t² . z = 2x – 5y, ly =s•t³ · t3

A: We find complex function

Q: dy : Find if dx 3.x 2) x - y 4+ y x +y 4) xy² x - y

A:

Q: dr. +37-10z

A: We have to evaluate the given integral.

Q: a) Find the equation of the plane th

A: The question is taken from the plane in which we have to find the equation of the plane and integral…