If y = 3 t2 – 4 t – 6 and x = dy sin (4 t) , find dx

Q: "ind for f(x.y) = x sin(y+ 3z) fe dz

A: The solution is given below

Q: find dy /dx for the following Y=sin x

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Q: d y(x) if e²-y = sin x. dx

A: Using implicit differentiation,

Q: dy solve for dx y = (x - 4 tan x)3,

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Q: Let y = cos(2x) 9x²+3 Calculate dy dx

A: Given function, y=cos(2x)9x2+3

Q: If y = tant and t = 4x³ + x, then dy dx 11

A:

Q: d²y dy and dx Find if x = sin 3z and y = tan23z dx2

A: It can be observed that both the variables x and y are the functions of  z, therefore to find the…

Q: dy Find for y = sin (2x +3) da %3D Ans=

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Q: If y=x2ex sin x,Find dy/dx

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Q: If x = yz and y = 2 sin(y + z), find dx/dy and d2x/dy2

A: Solution -    Given equation -  x=yz           .............................(1)y=2sin(y+z)…

Q: dy 2x-3 Find if y = dx tan 2x

A:

Q: Find dy for y = 5 sin dy= =dx 7x8 8

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Q: Find dy. Y= 6x/1+x2

A: Use quotient rule to calculate derivative of y that is dy.

Q: 2 x If y = x¯e" sinx,Find d

A:

Q: Find dx e 2X = sin (x+ 5y) %3D

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Q: Find dy dx x +3 Sint de X-x

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Q: (xr

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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.