B) Find (2) for the following functions: dx u? y = u² +1 u = 3x³ -2 at p (1,2)

Q: Find an interval of definition for the equation x^2 dx/dt = 3x^3 t^2

A: Domain of definition is where X(t) is defined

Q: Find dy/dx by implicit differentiation.   1) x3 + x4y4 + y7 = 5   2) x^2 / x+y = y2 + 7

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Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

A:

Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

A:

Q: dx y=u(1+u°)³ and u =(3x-2)². %3D Express the derivative in terms of x, if

A:

Q: integrate ​f(x,y)=x2−y over the curve​ C: x2+y2=4 in the first quadrant from (0,2) to 2,2.

A: The solution are next step

Q: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

A:

Q: Find dx/dt given that 4x^2+9y^2=13x  x=1,  y=-1 and dy/dt = 10

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Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

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Q: the linear approximation for f(x,y) = sqrt (y+cos^2 x) at (0,35) is ?

A:

Q: xy + 8y² = 4 d?y -(y/(x+16y)) dz?

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Q: (b) If f (x, y) = y sin2x + x°cosy °cosy 3 then verify dxðy dyðx

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Q: Differentiate the function. y= (5x- 1) (1-x°) dy %3D dx

A: Given that the function is      y = (5x-1)2(1-x3)4

Q: Find of/dx and dfldy. f(x,y)% 3 (3xy-1) of

A:

Q: Find dy/dx for the following functions:- (2) y = v sinh Vtan x (4) y=2,u = 3x²-2 u²+1

A:

Q: Find the differential of the function z=2x'y %3D

A: If z is a function of two variables defined by z=f(x,y) then the differential dz or total…

Q: |dx + N(x,y)dy = 0 x² + y,

A:

Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

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Q: В. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .

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Q: of of For the function f(x,y) = 4x* - 3y' - 8, find and dx of %3D dx of

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Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: dy - f *P, = 7 dt y(0) = 4.

A:

Q: 3 2 Find for y = dt, where x> 9t+2 dx dx

A: The given function is y=∫0x39t+2dt. Let u=9t+2. Then, du=9 dt. The upper limit will be 9x+2 and the…

Q: dy of y=X Find

A: y = x^x Find dy/dx

Q: Find the dy/dx by implicit differentiation. yvx +1= 4x - 2y 2(x+1) x+1 O Xxww wwxx 2y 2(x+1) x+1 O…

A: Given:  yx+1=4x To Find: To find dydx by using implicit differentiation.

Q: dy = 3 , find dt dx when x = 1 dt x and y are functions of a third variable t. If Væ + Vỹ = 4 and

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Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

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Q: Chose only two: dy 1. Find for y + In x2 y2 -cos 2x* = 27 dx 2x+1 2. Evaluate: f dx -4

A: We use chain rule and product rule while differentiating the given equation.  Also for integration,…

Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: 8. Find dy/dx in terms of x and y using implicit differentiaton 5y 4 +x 2 = 9

A: Step for implicit differentiation: (1) Differentiate with respect to x (2) Collect all the…

Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

Q: b) Find if dx2 d²y Lm Vt2 + 5 dt + sinx = y – x secx rsinx

A: We will first find the first order derivatives using Newton-Leibnitiz theorem. The , we will find…

Q: cos y f(x, у, z) -D xz2 XZ

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Q: Find fr and fy- f (x, y) = 8e dt

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Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: use implicit differentation to find dy/dx and d2y/dx2 at the point (1,0) for the given function…

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Q: Let y=f(x), Given dy/dx=(3x^2 -1)/(2y) with initial condition f(1)=4. Find f(-2)

A: Given y=f(x), dydx=3x2-12y⇒y dy=12(3x2-1)dx⇒∫ y dy=12∫(3x2-1)dx+C⇒y22=123x33-x+C⇒y=x3-x+C Now, to…

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…

Q: Differentiate the function. y=[(sx +2x+3) (x-3)]² dy dx II

A:

Q: Q4/ Evaluate (xy + e") dy dx using Three point formula in x,y-axis and two point formula in z axis

A: You must have an basic idea of double integral to solve this.

Q: Find the partial derivative. z = sin (9x'y – 10æy?) dz

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: