f f(x,y) = 8-2x3-6xy-3y2 and if x = (r-3)cos(s+1) and y = (r-1)/(r+s), using chain rule, find ∂f/∂r when (r,s) = (2,-1)

Q: Find the first partial derivatives with respect to x, y and z f(x. y.2) - 3x°y - 9 xyz + 10 yz² %3D

A: Given

Q: Find the first partial derivatives with respect to x, y, and z and evaluate each at the given point.…

A:

Q: If z=(X+Y) e and X-u * find the tollawing partial derivatives using Chain ruleo Express answers as…

A: Given, z=x+yeyx=u2+v2y=u2-v2 To find : ∂z∂u , ∂z∂v

Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = √u and u = x3

A: Recall the chain rule of differentiation:

Q: . Suppose that your best friend has calculated the partial derivatives of a given function f(x,y)…

A: Please see the below picture for detailed solution for detailed solution.

Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

A:

Q: Find the value of 0z/0x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation is xy + z3x – 2yz = 0 and defines z as a function of the two independent…

Q: Use the Chain Rule to evaluate the partial derivative at the point specified. ∂f/∂s at (r, s) = (1,…

A: Use the Chain Rule to evaluate the partial derivative at the point specified. ∂f/∂s at (r, s) = (1,…

Q: If z = (x + y)e and x = u? + v² and y = u? – v², find the following partial derivatives using the…

A:

Q: If F(x,y) =ln (x2y - xy2), find the partial derivatives Fx (3,2) and Fy (3,2)

A: Given:- Fx,y=ln x2y-xy2, find the partial derivatives Fx3,2 Fy3,2

Q: Find the value of at the point (1,1,1) if the equation 3xy +z°x-2yz = 2 defines z as a function of…

A: First do the partial differential in both the sides and then separate ∂z∂x and then put the value…

Q: Differentiate implicitly to find the first partial derivatives of z                              x2…

A: Given that function, x2 + y2 + z2 = 1 Differentiate with respect to x on both sides,…

Q: Differentiate implicitly to find the first partial derivatives of z…

A: the given implicit function is:xlny+y2z+z2=8

Q: Differentiate implicitly to find the first partial derivatives of w                           x2 +…

A:

Q: 5. Find the gradient of cos(xy) – 3y* + 3 at the point (1,4)

A:

Q: Find the value of ∂x/∂z at the point (1, -1, -3) if the equation xz + y ln x - x2 + 4 = 0 defines x…

A: Given equation is xz+ylnx-x2+4=0. Given point is 1,-1,-3. Partial derivative of given equation with…

Q: Find the first partial derivatives with respect to x and y of f(x,y) = (4x-y)/(4x+y) at the point…

A:

Q: Find the first partial derivatives of the function f(x, y, z) = xz – 5x²y³z*.

A: Find the first partial derivative of function f(x,y,z)

Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = u3 and u = √x

A: Given: ,and . Find out by using the chain rule.

Q: Find the requested partial derivative. dz z= (3x +4y) ; (2,5)

A: Option D is the correct option. Use the chain rule to find the partial derivative for z w.r.t x.

Q: Find the first partial derivatives of f(x,y) = 2 ex"y of II

A: Consider the given function. fx,y=2ex10y The objective of the problem is to find the first partial…

Q: Differentiate implicitly to find the first partial derivatives of z. 7x² + 3y² + 11z² = 36 əz əx əz…

A: Differentiate implicitly to find the first partial derivatives of z.   7x ^ 2 + 3y ^ 2 + 11z ^ 2 =…

Q: Find the partial derivative. z = (2² + 2x – 6y)"

A:

Q: Use chain rule to find given x² + 2y² + z² and x os (st), y %3D Cos

A: Solve the following

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

A:

Q: If  x2 + y2 + z2 = 9,   dx dt = 3,  and  dy dt = 5,  find  dz dt when  (x, y, z) = (2, 2, 1). dz dt=

A: If,  x2+y2+z2= 9 dx/dt = 3, and dy/dt = 5,  find  dz/dt when  (x, y, z) = (2, 2, 1). dz/dt=?

Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

A:

Q: Find the value of at the point (1, 1, 1) if the equation xy+ z°x – 2yz = 0 defines z as a function…

A: Given equation, xy+z3x-2yz=0

Q: Find the first partial derivatives for f(x.y)= 10x cos (3xy)

A:

Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: Differentiate implicitly to find the first partial derivatives of z. 7x2 + 5y2 + 2z2 = 25 az ax dz

A:

Q: Find the first partial derivatives for f(x,y) = x cos (5xy). of = cos (5xy) - 5xy sin (5xy) %3D of…

A: The solution for the above question is as shown below.

Q: 4. Given that c(t) = t² + 2, y(t) = t³ – 2t and f(x,y) = x² sin (xy). Using the df and evaluate it…

A:

Q: dz 1. dz ду || 2.

A: The given function is: z=(2x+7y)12.

Q: Find the first partial derivatives of the funct f(x, y) = x8 + 7xy5 fx(x, y) =

A:

Q: Use the Chain Rule to calculate the partial derivatives д(т, у) — sin (т? + у?), х— 4и — v, у — —…

A: Given g(x, y)=sin(x2+y2) ,x= 4u-v and y=-(2u+2v)

Q: (b) Find all first and second partial derivatives of z = x² In(x² + xy).

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find both first partial derivatives. z = cos(x2 + y2)

A: Given , z=cos(x2+y2)we have to find the first partial derivative

Q: b) Use the chain rule for partial derivative to find 2 when z = f(x, y) = x²y + ln(x + y) and (x, y)…

A:

Q: Find the first partial derivatives of fx and fy of the function f(x,y) = 4e2x - x3y5

A:

Q: If z = sin(x/y) and x = ln (u) and y = v^4, find the partial derivatives of z with respect to u and…

A:

Q: Q14. If V = f(2x – 3y,3y- 4z,4z – 2x) then apply chain rule of partial derivatives to prove that 6-…

A:

Q: Find the second order partial derivatives дхду of and дудх f(x,y)= 4x² + In x + e*** – cosy +9y +3.

A:

Q: Find the partial derivative of u = x^2 + y^2 + z^2 - 4xyz

A:

Q: 3. Find dy, where; (x+y) = 2 a) cos (xy)- + e b) e+ iPtany=1 , u= xlax (use chain rule)

A:

Q: Find the partial derivative. 2 = (r² + 5z – 6y)“ az ||

A: The given function is: z=x2+5x-6y4

Q: Find the 1st partial derivatives of z=(4x+6y)^11

A: Here we have to find partial derivatives by differentiating it with respect to x ( keeping y…

Q: Differentiate implicitly to find the first partial derivatives of w. x² + y² + z² - 7yw + 10w² = 9…

A:

Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

A: Given functions are