Given y = e 7x find dx Oy - 7xe7x Oy - 7ex Oy- 7e7x

Q: If x³ + 4x³y? = x – y³, find dy/dx. 3,2 | dy %D dx

A: Here we have to find the implicit differentiation.

Q: If ( 1 + x²)(1 + y²) - px² = 0, where p is a constant, show that xy ( 1 + x²)dy/dx = ( 1 + y²).

A: Given: To Find:

Q: Find dy for dx 1. e*y = e4x – e5y ху

A: exy=e4x-e5yDifferentiate with respect to yyexy+xexydydx=-5e5ydydx(xexy+5e5y)dydx=-yexy

Q: Find (d y/d x)& (dy/dx²) ex cosxy = y

A: To obtain dydx, apply chain rule and differentiate with respect to x on both sides of the equation…

Q: H.w: find dy dx 1- y=-10x+3cosx

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Q: (x*y - 2xy) dy dx 2.

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Q: So IVe the Pollowing D.E cx-DCX-と) +y dy メ ニ dx

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Q: Q2: If y=t? and x=3t-1 find dy/dx

A: y=t2, x=3t-1Formuladduun= n un-1

Q: Given y+In(-) = e dy then dx x(y+1)

A: Given: y+lnyx=e We know that ddxuv=vdudx-udvdxv2                                                 ..1

Q: d y(x) if e²-y = sin x. dx

A: Using implicit differentiation,

Q: dy dx y x y (1)=e-1 xe*

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Q: D cosh x dy + Cy Stnhx +e) dx - o +ě) dx =

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 7) y=-; x = 5, dx = Ax =-3 0.

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Q: If Y = f(x) = 6/x^3, find dy/dx? Select one: O a. (-18)/x^4 O b. (-9)/x^3 O c. 6X^2 O d. 18x^3

A: Sol:- Given:- Y=f(X)=6X3

Q: if y = (3x? + 4x – 7*)e, then dy/dx is:

A:

Q: Find dy dx dy if y dx = x³ + 8x + 6 x² - 5

A: Given: y=x3+8x+6x2-5

Q: (x - ky) dx +k(y-x)dy=0 where k 3t7

A: Given :(x-ky)dx+k(y-x)dy=0where k=7+3=10

Q: Find (d y/d x)& (d'y/dx²) ey cosxy = y

A: Here Hello. Since your question has multiple parts, we will solve first part (dy/dx) for you.…

Q: If xy3 + x3y = 2, find dy/dx at the point (1,1). a. 1            b. -1 c. 2             d. -2

A: Given that:-xy3 + x3y = 2To find : dy/dx at the point (1,1)Differentiation rules:power rule:…

Q: Find (d y/d x)& (d³y/dx²) ey cosxy = y

A: Giveny=exycos(xy)....(1)Differentiate above equation (1)  with respect to x by applying product…

Q: угах ру by Implicit ..חGLO! 7x2y + 4y?x = -5 dy/dx =

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Q: y = elx²+2x+3)2 y = ise dy =? dx

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Q: Find dy/dx of the given function. y = e 2x In x

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Q: a) Given: y = (x² + e*)(x + 4) derive dx

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Q: dy d. dx = y(xy3 – 1)

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Q: For the given DE: dy xy +y dx x2 – 5x + 6

A: Here we will find the value of y(x). We will gonna use a linear differential equation, L.D.E : dy/dx…

Q: c. x²dy+ (2x³y – e*)dx = 0 d. (2xy*e" + 2xy3 + y)dx + (x²y*e» – x²y² – 3x)dy = 0 е. 2х?ydx + ydx +…

A: As per guideline we can solve only one question at a time, so if you need more answers kindly repost…

Q: M(x, y)dx + (x² + x)dy = 0

A: Hint: The given equation is M(x,y)dx+x2+xdy=0. A differential equation M(x,y)dx+N(x,y)dy=0 is exact…

Q: x dy/dx + y = x³

A: Given differential equation

Q: D xy4dx +(y+1)E? dy =

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1. Find the dy of the followings: dx e* (i) y = x²lnx (ii) y = Inx (iii) y = (4x² – 20)(6x + 5) (iv)…

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Q: C dy X- dx X

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Q: If x = t+1 and y = t2 - 2t +3, then find t - 1 dx

A: We can find the answer using required rules as below.

Q: (a) Find dy if y= 1+2x² dx

A: We will differentiate w.r.t. x to solve 3(a).

Q: e'dx+ cosx dy 2. t.

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Q: 3. Find dy of the following equations: dx a. y = |(e-3x² + 7x² + In 8x

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Q: 5x find dy y = e4x dx

A: Given that y=5xe4x. Quotient rule of derivative: ddxuxvx=vxddxux-uxddxvxvx2

Q: L, L, x² e*y dxdy 1- 1

A: The graph of region of integration is as follows where orange part represents the area of…

Q: solve this D.E using separation of variables dy/dx = (xy+3x-y-3)/(xy -2x+4y-8)

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Q: Find the solution of the D.E. below: 2(2x + y)dx – xydy = 0

A: If a function f(x,y), satisfy the condition f(kx,ky)=knf(x,y), then it is called a homogenous…

Q: E: (y + x³y + 2x²)dx + (x + 4xy* + 8y³)dy = 0

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Q: - solve; dy A: dx e* * y3 x+1

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Q: S| (x? + y²) dx dy 'D Where D: x2 + y² x²

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Q: Find dy/dx for the given value of x y = In(x² – 8) ; x=4 A. 1 В. 2 C. 0 D. 3 Е. 4

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Q: * dy/dx+4y/x=6x-5 if y=1 and x=1 then C equal 1 -2 -1

A: The detailed solution is given below Thank you

Q: e*e>dx – e=2y dy = 0 - еx — е-Зу — с Зе* - е-Зу — с a. b. 3e* + e-3y = c e* +e-3y = c с. d.

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Q: Find for the given equation. dx x8 – y6 = x dy 1- dx

A: Differentiation

Q: d'y Find dx2 (a) y = 8x³ – 5x² + x dy dx? (b) y = 7x² – 2x + 9 - dy dx? x + 6 (с) у %— dy dx? (d) y…

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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.