dz A) – 2² f(u) – xzf'(u) 22 + x² f'(u) dz B) 2² f(u) 22 + xy f'(u) dz zf(u) – xzf'(u) C) dx 2² + x² f'(u) dz D) 2* f(u) + xzf'(u) 22 + x2 f'(u)

Q: Let x and y be differentiable functions of t and let s = 2x2 + y2 be the distance between the points…

A: Differentiate both sides with respect to t.

Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

Q: If z be a differentiable function of x and y and if x = c c cosh u cos v, y = csinh u sin v, then 1…

A: Given that z is a differentiable function of x and y and  x=ccosh u cos vy=csinh u sin v We will…

Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

A:

Q: Suppose that z = xy² and x and y are differentiable functions of t with x = 1, y = −1, dx/dt = −2,…

A: Given  z=xy2 Also at t=-1 x=1y=-1dxdt=-2dydt=3

Q: find the directional derivative of f(x,y,z)=3e^xcos(yz) at P(0,0,0) in the direction of A=2i+j-2k

A: First find out the partial differentiation of f(x,y,z) and then put the values (0,0,0) and then for…

Q: Suppose that z = x/y, where x and y are differentiable functions of u and v such that x = dx/dv 3, у…

A:

Q: Suppose that z = f(x, y) is differentiable at the point (27, 243) with f,(27, 243) = 3 and f, (27,…

A:

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 64) withf, (1024, 64) = 4 and f,…

A:

Q: Find and by implicit differentiation, and confirm that the - dy results obtained agree with those…

A: The solution is as follows

Q: Let f be a differentiable function of one variable, and let f(p), where p = (x² + y² + z²)'/2. Show…

A:

Q: Let x and y be differentiable functions of t and lets = sqrt(x2 + y2) be the distance between the…

A: Given that, s=x2+y2

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: 3r²y Determine if ƒ is continuous at (0,0) where f(r, y) = { r4 + 2y2 (x, y) + (0,0) (1, y) = (0,0)

A: for f(x) to be continuous at (0,0) limx→0+,y→0+f(x,y)=limx→0-,y→0-f(x,y)= f(0,0)

Q: Let f : R² → R with f(x,y) = x²+ y. Prove that f is differentiable at the point (0, 0)

A: Given function is f(x,y)=x2+y Since we know that, differentiability of function of two variable at…

Q: w that the equation of the tangent space of f(x, y,z)=Vx² +y° +z* at point (2,3,4) is 1 K, y, z) =…

A:

Q: Let f(x, y) be differentiable at (ro, yo). Then we have f(xo + Ax, yo + Ay) - f(xo, y0) fa (ro, yo)…

A:

Q: Let F(x, y, z) = (sin(xy), cos(xy), sin(xyz)). What is the divergence of F at the point (T, 2, 0)?…

A: Given : F→x,y,z = sinxy, cosxy, sinxyz

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given:     x2 + y2 = 100

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

A:

Q: What is the linearization L(x, y) of a function f (x, y) at a point (a, b)? How is L(x, y) connected…

A: Linearization L(x,y) of a function f(x,y) is given by the formula

Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),…

A: Given that      f(x,y,z)=ln(x2+3y2+9z2), P0(3,3,3), u=3i+4j Here we have to find the derivative of…

Q: 2. Prove that the directional derivative of f (x, y, z) = xy sin z at direction v = i+2j+ 2k is .…

A:

Q: Show that f(x,y)=exyx is differentiable at point (1,0) using the definition of differentiability.

A: A function is called differentiable, if the derivative of function exists at each and every point in…

Q: Let z = t*f (x, y) with f be a differentiable function. If x = t2 + u2 and y = t*u3, then ∂z/∂t…

A:

Q: c) Let f(r, y) = Vlry| Prove that f(r, y) is not differentiable at point (0, 0).

A: Given a function : f(x,y)=xy We need to show that f(x ,y) is not differentiable at (0 ,0). Let's…

Q: At what points (x,y.z) in space are the functions continuous? a. h(x,y,z) = In (2z - 4x – 5y3 – 1) 1…

A:

Q: x² sin +y f : R² → R, ƒ (x, y) = %3D x + y

A:

Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

Q: (a) Compute the derivative of the function F(x, Y, z) = x² + 2y² – 3z? at the point (1,1, 1) in the…

A: a) Given function F(x, y, z) = x2+2y2-3z2.    Point P(1,1,1).     vector v = i^+j^+k^ .      We have…

Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: I. Show that the function ƒ defined by (1, y) = (1, –1) f(1, v) = { +g (z, y) # (1, –1) + y is not…

A: We will use the sequential characterization of continuity to solve this problem. The detailed…

Q: Suppose that F(x,y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that дх…

A:

Q: Find the derivative of the function at Po in the direction of vector A h(x, y, z) = cos(xy) + e>% +…

A:

Q: prove that xy^2/x^2+y^2 is not differentiable at 0,0 when  xy^2/x^2+y^2 if (x,y) not equal to (0,0)…

A:

Q: Let f(z)=ex^2 = U(x,y)+iV(x,y) Verify Ux=Vy

A:

Q: Suppose z = f(x, y) is a differentiable function of x and y, x =r cos 0, and y =r sin 0. (a) Compute…

A:

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) with f,(1024, 1024) = 5 andf,…

A:

Q: Suppose that z is a differentiable function of x and y with dz (1, 1) = 162 and(1, 1) = 6. dz ду dx…

A:

Q: Suppose r lIs a differentiable function of x and y, and g(u, V) = (e sin(V), V)). Use the table of…

A:

Q: is function oF x $ y xz + y In x = ze-sin (xy) D. Ausumo that z Find zx iF

A:

Q: Suppose that z is a differentiable function of x and y with dz (6, 1) = 35 and(6, 1) = 7. dy dz Ifx…

A:

Q: Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (z*+6y") a) Show that (0, 0) and (0,0) exist. dy…

A:

Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

A: Given equation is s=x2+y2. Compute the derivative of s with respect to t.…

Q: Find f and fy- f (x, y) = 9e dt f (x, y) = %3D fy(x, y) =

A:

Q: Suppose that z is a differentiable function of x and y with dz (8,7) = 80 and dx dz (8, 7) = 2. ду…

A:

Q: Study the continuity of f(x,y) = xe-Vx at p(1,0) ey.

A:

Q: Find fr and fy- f(x, y) = ets dt %3D f (x, y) = %3D fy(r, y) =

A: