Find the linearization L(x) of the function g(x) = rf(x²) at z = 2 given the following information. f(2) = 0 f'(2) = 6 f(4) = 3 f'(4) = -2 Answer: L(x) =

Q: Find the first partial derivatives for f(x,y) = 5x cos (5xy).

A:

Q: Find the first partial derivatives of the function

A: NOTE : As you have uploaded multiple questions without specifying which one to solve, we will answer…

Q: f(x, y) = ln(x + y)

A: for the first order partial derivative we have to find fx = derivative of f with respect to x fy =…

Q: Find the four second partial derivatives of the following function. f(x,y) = ln (3x2 + 4y2 + 7)…

A: We have to find

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: Find the second-order partial derivatives of the functions ƒ(x, y) = x + xy - 5x3 + ln (x2 + 1)

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Q: compute the first-order partial derivatives. z = ln(x2 + y2)

A: Consider the given function z=lnx2+y2 We have to find the first-order partial derivative. ∂z∂x, ∂z∂y…

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: 5. Find the differential equa tion of (x-c.)" †C2Y C3

A: We will eliminate the arbitrary constants. As there are 3 constants so it'll be differentiated…

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A: To find - Determine the orthogonal trajectories of the family of electric field lines described by…

Q: Find all the second order partial derivatives of the function : f(x, y) = ln 4xy + sin 3xy + e1x-3y

A: We need to find the second order partial derivative of the function

Q: 2. z = x + 2 У Х x

A: Solution

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

A:

Q: Find the first partial derivatives of the following function. 2s - 3t f(s,t) = 4s + 5t

A: We have to find the partial derivative

Q: Find the first order partial derivatives of the function, w=xz-5(x^2)(y^3)(z^4)+ln(x*y^2*z).

A: w(x,y,z)=xz-5x2y3z4+ln(xy2z)

Q: Q3:Find all the second order partial derivatives of the f(x, y) = 2x*- 5x'y3-y

A: Given: A function fx,y=2x4-5x3y3-y3. First, find first-order partial derivatives fx by…

Q: z = x3 – xy? + 3y² |

A:

Q: Find the first partial derivatives of the function. z = (7x + 8y) az !! ax %3! ду

A:

Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

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

A:

Q: Compute the partial derivative if z = A) - 3ry? B) 1 C) D) Does not exist.

A:

Q: 4. Given y = 3u² – u and u = x³ – 1, use the Chain Rule in Leibniz notation to find the value of dy…

A:

Q: Find the first partial derivatives of the following function. f(x,y)=x²-3xy-6y²

A:

Q: 3. z = x+y x-y

A: Given:        z=x+yx-y Partial derivative with respect to x:      ∂z∂x=∂∂xx+yx-y      Treat y as…

Q: v = ) V In(2x-3y

A:

Q: Find the first partial derivatives of the following function. g(x,y) = cos ° (x°y³) ag

A: I have used chain rule for derivative

Q: In x Find the linearization of f(x) = xmª around x = e. Round the gradient and y-intercept, whenever…

A:

Q: 1. u= x² + y² + z²

A: On solving this we will get

Q: 3. z = x+y x-y

A: The given function is  z=(x+y)/(x-y).

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 first partial derivatives of the given functions. z = x3 - xy? + 3y?

A:

Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

A:

Q: Find the first and second-order partial derivatives of f (x, y) = x - 9x²y+ 3xy af b)

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: Find the first partial derivatives of the following function. f(x,y)%3D2x

A: Given,  f(x,y)=2x8y

Q: f(x.y.2) = x²yz° + xy - z

A: To  Find the first partial derivatives of the given function

Q: 1. Find the orthogonal trajectories of the family of curve z² + 3y which is passing through (10,…

A:

Q: If f(x, y, z) = 2x5 + 3y5 - 8x3y²z², what is the partial derivative of f with respect to x? (A 10х4…

A:

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

A:

Q: Compute the indicated partial derivative. g(x, у) %3 сos(x + ) 9xxy

A:

Q: Find the first partial derivatives of the function. f(x, у) = 3x + 5y + 4 fy fy

A:

Q: Find the first partial derivatives of the given functions. 1. z = x3 – xy? + 3y?

A: SOLUTION-

Q: find the partial derivatives of l(BO,B1) Σ 2 i=1 yi log ( 17 1² (B₁ + B₁ x)) + (1-y₁ ) log (1-² (B₁…

A: As per the question we are given a function l(β0 , β1) in partial summation form and from that we…

Q: Find both first partial derivatives. h(x, y) = e−(x2+y2)

A: The given function is hx,y=e-x2+y2. To find the partial derivatives. Solution: The given function is…

Q: 1. z=x - xy + 3y ?

A: Given: z = x3-xy2+3y2 To find: The first partial derivatives of the given function.

Q: Find the four second partial derivatives of the following function f(xy)-In (7x2 + y2 +9)

A: To calculate all the second order partial derivatives of the given function of two variables

Q: If z = xy2 + 6x, then y2 + 6 is the first order partial derivative of z with respect to x. O True…

A:

Q: Find the partial derivative with respect to z of the function (3a – 2)e2y-5 In(-5z - 1).

A:

Q: Find all the second-order partial derivatives of the functions w = x sin (x2y)

A: Given function is w=xsinx2y. To find all the second-order partial derivatives of the function.…