2. Let 1 f(x): Recall: L(x) = f(a) + f'(a)(x - a) and L(x) f(x) when x is close to a (a) Find the linearization L(x) of f at a = 1.

Q: 2. 2. Let そニと X=UV, y = sin v, Use ナ chain chain Rule to find Ev.

A: 1) The given function z=e2x2y+3xy2 Differentiate with respect to x taking y as constant…

Q: 1- Find the mixed partial derivative: w = e* +x In(v)+y ln(x) %3D

A: Given,        w(x, y)=ex+xln(y)+yln(x)

Q: Let h(x, y) = , x = 8t t2, y = 7tt2. %3D Use the Chain Rule to calculate the partial derivative.…

A:

Q: Find the linearization L(x) of y = e In(x) at a = 1. L(x) = %3D

A: Given a function f(x)=y=e3x ln(x) To find the linearization L(x) at a=1 The linearization L(x) is…

Q: If f(x, y, z) 2x5 + 3y5 — 8x2у?z?, - what is the partial derivative of f with respect to z? .A f z =…

A: Partial differentiation of  F(x,y,z) = 2x⁵ +3y⁵ - 8x²y²z² with respect to z

Q: 1-Find the mixed partial derivative: w = e* +x In(y)+y ln(x)

A:

Q: Find all the first and second order partial derivatives of f(x, y) = - Vã+ In y. x3

A: While finding the partial derivative of a multivariable function, if we have to find the partial…

Q: Find the partial derivative of z with respect to x (32) for z = (3x² + 1) cos(x²y) O None of the…

A:

Q: 9. Find all second order partial derivatives for the following functions: a) z = xe-2y + x In(y) + y…

A:

Q: 2. The second order partial derivatives Fxx(x,y) of the function ( F(x,y) =x'y- In (x'-y)) equal .

A:

Q: 12.) Compute the first partial derivatives of the following function. f(x,y) = 2- tan 1 (7x² + 2y²)…

A: The given function isf(x, y) =2tan-17x2+2y2to find partial derivative fx, fy

Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

A:

Q: For z = arctan(x² + y²): Compute all first and second order partial derivatives. Find the…

A:

Q: (b) Find the first order partial derivative af and for the function f(x, y) = x/y –x²y+ y²

A:

Q: Find the first partial derivatives of the following function. s(xz)-z2 tanxz

A: The given function is s(x, z) = z2 tanxz.The first partial derivative of the function s with respect…

Q: of For the function below, use the limit definition of partial derivative to compute and at ôx…

A:

Q: Compute the indicated partial derivative. g(x, y, z) = x³y^z° 9xxyz =

A:

Q: of ) Find the first order partial derivative of and for the function f (x, y) = x/y -x²y+y² ây

A:

Q: Compute the indicated partial derivative. g(x, y, z) = x³y^z° 9xxyz %3D

A:

Q: 1. Consider the function z = x In(1+ y²), if x 2-t and y= Vf, use an appropriate form %3D dz at t…

A:

Q: If f is a function of x and y such that fxy and fyx are continuous, what is the relationship between…

A: Function: fx and fy are continuous function. Let us choose f(x,y)=x3y3+πxy Here fx=3x2y3+πy…

Q: Find the partial derivative of z with respect to x z = (3x² + 1) cos(x²y). əz = -2x (3x² + 1)…

A: Given function z=(3x2+1)cos(x2y)

Q: Let f(x, y, z) = 4xy – z², x = 6r cos(0), y = cos (0), z = 3r. Use the Chain Rule to calculate the…

A:

Q: Check whether the given function is satisfying the Fubini’s theorem about mixed partial derivative…

A: We have to check whether the function fx, y=3x2sin4xy satisfies the Fubini's theorem about mixed…

Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

A:

Q: 1- Find the mixed partial derivative: w = e* +x In(v)+y ln(x)

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

Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

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: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

A:

Q: Let f(x, y, z) = 6xy- z, x = 3r cos(0), y = cos (0), z = 3r. Use the Chain Rule to calculate the…

A:

Q: 2) Find all the second-order partial derivatives of the functions: a. f(x, y) = tan (-)

A:

Q: Find all the second partial derivatives of Z; given: a) Z = xy³In(3XEY )

A: The given function is, Z=xy3ln3xey Determine the first derivative of Z with respect to x.…

Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: Given function f(x, y) = 1+ xy - x - y. df a) using partial differential involving limits to obtain…

A:

Q: If f(x, y, z) = 2 sin(100xy) In(2), compute the value of the limit f(1, h, e) – f(1,0, e) lim h→0 h

A:

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: 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: 4. Find all the second-order partial derivatives of f(x, y) = 2ry In(r+ y).

A:

Q: 4. If R(T) is the autocorrelation function of a stationary process {X(t)} with no periodic…

A:

Q: 5 The function f(x, y) = | x' cos is homogenous inx and y of degree

A: Given that: f(x, y)=x2cos2yx-y2+x3y

Q: If z = f(x,y) = tan x =t cose and y =t sin@. Use the Chain Rule method to find y as functions of t…

A: Given that z=f(x,y)=tan-1xy Where x=tcosθ,y=tsinθ Substituting, the values,…

Q: 19. Given w x³ + ln(3x − 5y²), find the partial differentiation for x and y.

A:

Q: 1. Use the definition of partial derivative as the limit of a difference quo- tient in order to…

A:

Q: Find all second partial derivatives of Z e

A:

Q: b- Use Chain Rule to compute w = 2y e* - Inz } əw at x = ln(t² + 1), at (t) equal to (1) for: y =…

A:

Q: Find the first partial derivatives for z = xy In (xy)

A:

Q: Consider a Lorenz curve given by f(x)=x^n for 0≤x≤1 and n≥1. What happens to the Gini index G.I as…

A: Consider the given function. fx=xn The Gini index is defined as, GI=2∫abx-fxdx

Q: Let f (x, y) = x3 – 3xy + y3. Find all critical points of f and at each critical point, - use the…

A: Critical points using second derivative test