dx dx Find - - for x = x(t) defined implicitly by V +V x In(t) = eVxt. Also dt evaluate at %3D dt (t, x) = (1,1).

Q: Give xy+x^2 y=2 such that dx/dt=2 in/sec. FInd dy/dt for x=1

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 8x3/4 %D dy =

A: given y = 8x34  we find the differential dy of the above function.

Q: dx dy Find at x = 1 if y = – 5x´ – 3 and 5. - dt dt dx dt

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 7x2 – 3 dy =

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Q: Find the total differential dw. 1 5. w = x tan¬' y – 2ªyz -

A: Solved below

Q: Find the differential dy of the given function. (Use "dx" for dx.) y dy

A: use chain rule while differentiating

Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 5 y%3D 2x - 5 dy =

A: Given:y=x+52x-5Differentiation formula:ddxxn=n.xn-1ddxuv=vdudx-udvdxv2

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

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Q: 20 dv on the interval [0, 20] dt du dt 20

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 3Vx + х dy =

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Q: Find the differential dy of the given function. (Use "dx" for dx.) = 8x3/4 dy = %3D

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Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

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Q: Find the value of dy/ dt at t = 0 if y = 3 sin 2x and x = t2 +π.

A: Given : y=3sin2x, x=t2+π To find : dydt We can write dydt as, dydt=dydx×dxdt                    1…

Q: Suppose that x=x(t) and y=y(t) are both functions of t. If x2 + y2 =17, and dx/dt=2 when x=4 and…

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Q: w =sec (xyz) - Yx +y+z

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Q: 1. Use the Improved Euler's method to integrate dx = t - sinx dt given x(0) = 1, using a step size…

A: The given differential equation is dxdt=t-sin(x), x(0)=1, h=0.1 The formula for improved Euler…

Q: dx at x = dt dy Find - 5 if y = x² - 3 and = 4. dt

A: A detailed solution is given below

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

A:

Q: given xy+x2y=2 such that dx/dt=2 in/sec. Find dy/dt for x=1

A: Consider the equation and

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = - cos( 7x - 1 dy =

A: We have to find dy for the given function y=17cos7πx-12.

Q: Use the Chain Rule to find dz/dt. dz dt || z = √√√ 1 + x² + y², x = 2 In(t), y = cos(t) 1 √1+ (Int)²…

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Q: Given: y=fso(x-1) dt - dy =D{(x). dx show that

A: We will prove the following result using Leibnitz rule.

Q: 4. Find the double integration of [(1+xy* )dx dy. ww m

A: The given integral is ∫04∫y2y(1+xy2)dx dy

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 7x2 − 3 dy =

A: Given y=7x2-3 Differentiating both sides: dy=14xdx

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 8Vx + dy

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Q: dz Find dt if z = x²y – sin y, x = vt? +1 and y = e -

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = (x+1)/(3x-5)   dy=

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Q: Find the differential dy of the given function. (Use "dx" for dx.) 4 y = 8V dy

A: We can make it easier for you.

Q: dy Find at x = dt dx - 1 if y = 2x? – 3 and dt - 2. dy dt ||

A: y = 2x2 - 3dxdt = -2dydt = ?   at x=-1

Q: What is the integrating factor of the non- exact DE (4ху+ 3у?-х)dx+x\x+2y)dy %3D0 ?

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Q: 1. xy + z2

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Q: Find dy/dt using the given values. dy dt y = x² - 6x for x = 1, dx/dt = 3.

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Q: a) dx dt dy dt =x+√3y+et √3x-y+e³t = ||

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: Find dy/dt when x=4 and dx/dt=-3, given that x^3+y^3=72

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Q: Given xy+x 2y =2 such that dx/dt = 2in/sec. Find dy/dt for x=1.

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Q: Aparticle moves on the graph of y^2=x+1 so that dx/dt=4x+4 what is dy/dt whrn x=8?

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Q: Hello! Can you help me with this calculus problem?

A: Write y using exponent Then differentiate both sides. Use power rule and chain rule on the right…

Q: Find dy/dt using the given values. y = x - 3x for x = 4, dx/dt = 4. dy dt

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = xV9 - x2

A: Use  the differential of the form f = u.v

Q: 3 Find dy for y= +3) dt dx

A: Given,

Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 4x - 7 dy

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y 3 x dy =

A: Given function can be written as

Q: If y = x2 and dx/dt = 3, then what is dy/dt when x = -1?

A: Differentiate both sides with respect to t.

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 9Vx+ dy =

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 4x + (sin(x))² dy

A: The solution is given below

Q: THE IVP

A: Consider the provided differential equation with initial condition is,

Q: If x^2+y^2=25 and dx/dt=6, find dy/dt when y is positive and (a) x=0: x=1 x=4

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.