Find the linearization L(x) of f (x) = tan x at a =

Q: 1. Find the first partial derivative of z with respect to x if x'y+ y°z+ z'x = 11.

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Q: Find the partial derivative. z = sin(9x°y – 10xy²)

A: Given: z=sin9x3y-10xy2

Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: Find the partial derivative of f with respect to x of the function f(x,y) =xy(e^x3)+y

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Q: Calculate the derivative e12x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.

A:

Q: Compute the following derivatives using the chain rule. g(y) = ln(1 + y).

A: Take 1+y = t  And use chain rule

Q: Find the linearization at x = a. IT f(x) = sin³ (x), a = 4

A: Given,            The linearization at x=a.             fx=sin3x, a=π4We know that,             The…

Q: If f(x, y) = y² cos(x) – a° In(y), find the second partial derivative

A: Partial derivative problem

Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-1

Q: Find all the second-order partial derivatives of the functions w = x2 tan (xy)

A: Consider the given function: Here the objective is to find all second-order partial derivatives of…

Q: Find the partial derivative. f(p, q) = ev af

A: From the given problem; fp,q=e6pq As we know that: The chain rule: fgx'=f'gx·g'x The Power rule:…

Q: Let f(x, y) = exy and P(1, 0). Find the maximum and minimum rates of change of f at the point P. In…

A: Given function is: f(x,y)=exy and point P(1,0)

Q: Find the gradient of f(x, y) = y ln x + xy2 at the point (1, 2).

A:

Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

Q: Find all second partial derivatives of z=(e^x)(tan y)

A: Topic- Partial Differentiation

Q: Find the derivative of the function at Po in the direction of A. 1- f(x, y) = 2xy - 3y² , Po ( 5,5),…

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: Let f(x, y,z) = z-sin(xy), x t, y Int, z et1. Find derivative of f directly and by using chain rule…

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Q: Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).

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Q: Find the partial derivative. z = sin(2.a*y – 3xy?) az

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Q: Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

A: The solution is given as

Q: Let f (x,y,z) = xln(yz). Find the maximum rate of change of f at the point (1,2,;) and the direction…

A: Suppose f  is multivariable function as f=fx,y,z then gradient vector is a vector that is composed…

Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In( 6 x - 3 y), Po(-7, -4…

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Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: Find the derivative of f (x y z) = x^3 − xy^2 − z at (1, 1, 0) P0 in the direction of A = 2i - 3j +…

A: Given,           f(xyz)=x3−xy2−z  and point Po =(1,1,0) and the direction vector A=2i-3j+6k.

Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: Calculate the derivative d dæ In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A: First, we split the integral function into two terms. Now find the derivative of both integrals by…

Q: Let f(x, y,z) = z-sin(xy), x = t, y = ln t , z = e^(t-1) . F

A:

Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: Use the second partial derivative test to find the relative extrema of f(x,y) = -x³ + 4xy 2y2 + 1.

A: The given function is  f(x, y)=-x3+4xy-2y2+1

Q: Express the autocorrelation function of the process {X'(t)} in terms of the autocorrelation function…

A:

Q: Use the Fundamental Theorem of Calculus to find the derivative. Vx-x1-t2 dt d dx

A: The Fundamental Theorem of Calculus says: ddx∫ag(x)f(t) dt=f(g(x))·g'(x)...(1)

Q: Find the derivative of the function at the given point in the direction of A. 3) f(x, y, z) = -10x+…

A: Here initially we need to find out the partial derivative of the given function to find out the…

Q: Find the partial derivative. f(p, q) = e=

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Q: Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.

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Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: Find the linearization of the function at the given point. f (x, y) = e sin y, 0, 7).

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

Q: Find the linearization of the function f(x,y) = y + sin (x/y) at the point (pi,3)

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Calculate the second-order partial derivative of f(x.v) =sin(x³v?) with respect to x and y, that is,…

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Q: Let f(r,y, z) = x² + 3x°y + z°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x) = 3t…

A: By fundamental theorem of calculus, we have

Q: (or axay дудх Calculate the second-order partial derivative of f(x.v) = xy with respect to x and y,…

A: Given  f(x,y)=xy

Q: Find the partial derivative of the given u = In[x?e*Y].

A:

Q: 1. How do you find the linearization of f(x) at x = a? Illustrate with a concrete example

A: We have to solve

Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))