If f(x) = x(e*+=') , then f'(x) = %3D %3D (A) (e² + æ³) æ(e*+z*-1) (B) (e" + 5æª) In(x) æ(e*+a*) (C) (e² + 5æª) In(æ) + +z° (D) (In(x) + tr") æ(e*+x") (E) ((e" + 5xª) In(x) + +x") æ (e* +x*)

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: equilibrium

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Q: (a) Apply first principles, to calculate the differential coefficient of (x) = 5(3x²+2) when x = 3.

A: Solution a: Given function is f(x)=5(3x2+2) using first principle…

Q: x-1, X)1 find the generol solution of the differential eguation below

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Q: If N(x) = sin x – sin θ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. (SOLVE BY…

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

A: Partial derivative problem

Q: If f(x, y, z) 2x5 + 3y5 - 8x2y2z2, what is the partial derivative of f with respect to z?

A: The given function is fx, y, z=2x5+3y5-8x2y2z2.

Q: ne following second-order differential equa

A: Introduction: A second-order differential equation has a form d2ydx2+p(x)dydx+q(x)y=r(x), where…

Q: 2. z = x + 2 У Х x

A: Solution

Q: What do you mean by Polynomial Differential Operators?

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

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Q: ӘТ ӘР V

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Q: Solve the differential equati on. dz (log x) = –(log z) dx X

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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: 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: Find the differential equation of the family of parabola with vertex and focus on the x-axis

A: The given question is related with parabola. We have to find the differential equation of the family…

Q: Find both first partial derivatives. g(x, y) = ln√x2 + y2

A: Given function is gx,y=lnx2+y2 Partial derivative of function is derivative of function with one…

Q: A certain population is known to be growing at a rate given by the logistic equation = x(b – ax).…

A: Firstly find critical points. After that find second derivative , If second derivative less than…

Q: Find a differential equation of the family of parabolas with vertex on the y-axis, with axis…

A: Let the vertex is at a point (0,k). Then, the expression of the family of parabolas with axis…

Q: Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N =…

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Q: Is the differential equation x" + e^x - 1 = 0 conservative or non-conservative? Explain why? If it…

A: Given x''+ex-1=0

Q: In a city of a fixed population of "P" people , the rate of change (with respect to timet) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to…

Q: f f(x) = ex – e-x – 2x and g(x) = x – sinx, evaluate the limit of f(x)/g(x) as x approaches zero.…

A: Here we have, f(x)=ex-e-x-2x and g(x)=x-sinx We have to evaluate limx→0f(x)g(x)=?

Q: Suppose a student carrying a flu virus returns to an isolated college campus of 3000 students.…

A: Total no. Of students=3000 And x is the no. Of students interacted with the flu.

Q: Find the partial derivative fx ( x , y ). f ( x , y ) = x ln ( 3x + 4y )

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Q: If y = f(x) is a function satisfies the differential equation f'(x)x³ + f(x)3x² = x³ ,where C…

A: We have to solve the given differential equation and find f(x).

Q: n In a certain tropical forest, litter (mainly dead vegetation such as leaves and vines) forms on…

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Q: A spring has a mass of 10 kg, is underdamped with coefficient β = 5 and its frequency is 0.8 Hz.…

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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: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

Q: 2. A company has contracted to manufacture 10,000 closed wooden crates having dimensions 3 m, 4 m,…

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Q: Find the partial derivative. = (a² + 4x – 2y)° - dz II

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Q: 3. The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Here we will use two formula  1st Area of triangle  If two sides of a triangle has length a and b…

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 differential of y² + x = 4.

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

Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

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Q: 2] write the chain rule formula for the derivatives Of and E , where Z=ZCrisit).

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Q: A differential equation is said to be exact when ∂M/∂x=∂N/∂y where M and N are its corresponding…

A: Consider the following differential equation: 3x2y-lnx+3ydx-2lnx+xy-3dy=0 M=-2lnx+xy-3N=3x2y-lnx+3y

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

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

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Q: Find all first partial derivatives. z = ln(x2 + y2 + 1)

A: Given The equation is  z = ln(x2 + y2 + 1) .

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…

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Q: Find the differential equation of Parabolas with vertex on the x-axis, with axis parallel to the…

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Q: 4. What is the total differential dW given W In(x+y +z)? 5. A light is hung 15ft above a straight…

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Q: The implementation of a good harvesting policy for fisheries is crucial to ensure a sustainable…

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Q: (b) Find the partial derivative, g where g(x,y)=sin' (2x+y). (c) Given z= In(2x+3y) with x 2s' (t-s)…

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