"For a continuous function f(x), defined on an interval a , b, we have d f(x) dx = f(x), dx a because integration and differentiation cancel each other."

Q: Find the differential of the function y = f(x). 2x2 + 5 f(x) = X + 5 dy = %3D

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Q: Find the total differential. z = e-X tan(y)

A: Given, fx=z=e-xtany To find fx=z

Q: That the value of the integration g(1) = 00 , g(2) = 0 1-e t) -dt 9(t) where g is a function that is…

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Q: We are given the function f(x,y)=sin(3x+2πy)+exy-π, and points A(π, 1), B(π + 1, 0). Find the rate…

A: Given function is, fx,y=sin3x+2πy+exy-π. To find the rate of change of f at A(π,1) along the…

Q: hi, i've added the problem as a picture please take a look. thanks in advance!

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Q: Find the implicit deriviate (dy/dx) of (2x+3y)1/3=x2

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Q: cos x + sin y = e e`ty

A: Given,          cosx+siny=e-xy

Q: Find dy for all of : dx 1- y = x/Inx у

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Q: Find the differential of the function y = f(x). f(x) %3D X - 8 dy = %3D

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Q: 1. Find the total derivative dz/dy, given (a) z = f(x, y) = 5x + xy - y2, where x = g(y) = 3y² (b)…

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Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx s2n?…

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Q: Find the value of the derivative of ƒ(x, y, z) = xy + yz + xz with respect to t on the curve x = cos…

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Q: Find the differential dy of the given function. y sec² x x² + 2 dy sec²x(x²+2)tan x-x (x² + 2)² dx X

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Q: Find the differential of the function y = f(x) f(x) = (2x² 1)1/3 dy = %3D

A: It is derivative problem.

Q: If f(x, y) = y cos(x) – x* In(y), find the second partial derivative (A dx? -y? cos(x) – 6x In(y) d…

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Q: Find the most general antiderivative of the function. f(x) = + 3 cos x

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Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a ,b],…

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Q: Let y = f(x), where f(x) = 6x2 + 3. Find the differential of the function. dy =

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Q: 4. Supposea function y = f(x) is so be revokved at x = e from point (a, b) to (c, d), what is the…

A: Please refer the attached image for complete solution.

Q: In integrating the function fx' In Sx dx using integration by parts, what would you choose for your…

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Q: 1. By using the differentiation method, evaluate the following integrations whether the are true or…

A: According to power rule of differentiation , and according to product rule of differentiation  ..

Q: Oppgave 1 Regn ut integralene (dersom de eksisterer). Sre [x² x cos(x) dx S In(x) dx x7 15 1/√ √…

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Q: Let y = f(x), where f(x) = 3x+6/x+6 Find the differential of the function. dy =?

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Q: Determine the total differential (dg), and total derivative with respect to x 3x 2y f(x, y, z) =…

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Q: Find the differential dy of y = tan x for x = π/4 and dx = −0.1.

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Q: Suppose that x and y are both differentiable functions of t and are related by the given equation.…

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Q: 4. Evaluate e*dx using integration by parts.

A: Explanation and solutions is given below.....

Q: (b) Evaluate f 3æ“ In6x dx using integration by parts.

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Q: What is the derivative of this integral?

A: We know that

Q: Find  dy/dx by implicit differentiation. x2/x+y = y2 + 4

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Q: If f'(x) = 5x*, what is f(x)? (Use C for the constant of integration.) f(x) =

A: To find the integration

Q: Find the differential dy of the given function.    y = x tan x

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Q: Integrate f dx using integration by parts. x+1

A: Please refer the attached image for complete solution.

Q: Find by implicit differentiation : arctan (xy)= y+x²y . dx

A: Given arctan(xy2) = y +x2y   We have to find dy/dx

Q: Find the differential dy of the given function. y sec² x x² +2 dy = sec²x(x²+2)tan x-x (x²+2)² dx x

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Q: find the integration of f x'e* dx

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Q: Find the differential dy of the given function. (Use "dx" for dx.) 8 y = 2√x + 4 dx *- (√x +++1)x dy…

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Q: Find F'(x). 2x F(x) = cos(t*) dt

A: If f(x) is continuous over an interval [a, b], and the function  F(x) = ∫au(x)f(t) dt then F'(x) =…

Q: Determine the most general antiderivative:  f(x) = sec x tan x-2e^x

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Q: Find dy/dx by implicit differentiation. tan(x − y) = y / (3 + x^2)

A: I have stated the used formulas in the solution.

Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: dy 3 (49-y²) 2

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Q: Find the differential dy of the given function. sec² x y x² + 2 sec 2x (2x²tan x + 4 tan x-2x)…

A: This question is based on quotient rule

Q: Suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: Consider the equation 5xy-5x3=15 Here, the objective is to find dydt in terms of x,y, and dxdt

Q: Let y be a function of x and y' = dy/dx . By implicit differentiation, compute y′ from each of the…

A: Here we have to find the derivative. a) yx2-y2=3b) y2x+x2y=y

Q: Change the order of integration. "A/2 x + 1 3 sin(x) dy dx

A: Consider the graph:

Q: 1. If f(2) = 1, find the constant of integration for dx f(x) = +3

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Q: b)x > 0 impending all continuous f function | f(t)dt = x. arctan(x) f(1) =?

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Q: If f'(x) = x*, what is f(x)? (Use C for the constant of integration.) %3D f(x) = %3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.