dy Q1) Find dx for the following function x²(x² + y²) = y²

Q: - Find dy /dx for the given function y? cos fy)=2x +2y

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Q: Find dy/dæ in terms of t if x =t – t°, y = 2+ 4t dy/dx =

A: The differentiation of parametric form of functions can be done by using the formula,

Q: dy In(3x + 7) Find for y = dæ 9e5z dy %3D dx

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Q: dy satisfies dx? 2 iven by

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Q: Find dy/dx, where y is a function of u such that dy/du = u/(u2 + 1). State the answer in terms of x…

A: we need to find dy/dx, Where y is a function of u such that dy/du = u/(u2 + 1)...(1). State the…

Q: dy Let y = f(x) such that In(x – y) = 2x – y + e². Find dx

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Q: dy when t = 7. dx Evaluate y = 2z? – 3z + 5 x = 4t +t t = z? +z+1

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Q: dy Find for the following function. dx y = 5 sin x cos x dy dx II

A: We have to find the derivative of given function. We will use formula for product of function.

Q: Find dy/dæ in terms of æ and y if æ°y – x – 2y – 1 = 0. dy dx

A: We have to find dydx in terms of x and y if x3y-x-2y-1=0.

Q: Find dy/dx for the fo d) x' + x.tan y = y -1

A: There are multiple question, As per our company policy ask other question separately. d.

Q: Given y=squarerootx.  Find dx/dt when y=8 and dy/dt=1.75

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Q: If x = 2t2 +t+1 and y=8t3+3t? + 2 then dy at t = 1 is dx

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Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

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

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Q: Find dy/dx and d2y/dx2 of x= t + 1/t, y= t + 1

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

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Q: Use the attached equation to find  dy/dx for this: 5tan−1(x2y) = x + xy2

A: Given, 5tan−1(x2y) = x + xy2

Q: dy Q5: Find for the following functions: dx (3) y = et sin²x In√x

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Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: dy Find ax for the following function. y = x cos x sin x dy dx

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Q: Find Dy/Dx given that y= x1-x

A: Given that y=x1-xwe have to find dydx

Q: Find dy/dx, where y is a function of u such that dy/du = u/(u2 + 1). State the answer in terms of x…

A: Find dydx.

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

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Q: dy Find for the following function. dx 5- cos x y = 6+ cos X

A: To determine the first order derivative of the function.

Q: dy Find for y = /12+13t dt. dv

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Q: Q2: Find the for the following functions: dy dx 1. y = 1- and t = 1/ 2. y [In(x² + 2)²1³ 3. y = xsex

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Q: Evaluate dy/dx when t = 7 such that: y = 2z^2 - 3z + 5 x = 4t^3 + t t = z^2 + z + 1

A: Given                y=2z2-3z+5           (1)    x=4t3+t                   (2)    t=z2+z+1…

Q: dy Find for the following function. dx y = 5 sin x+2 cos x dy dx II

A: Given that          y = 5 sinx + 2 cosx  Here we have to find dy/dx .

Q: dy if y = vt' -e' and x = dx Determine In(6t)

A: dy/dx = [7/2 t^5/2 - e^t] [ln(6t)]^2/ t^2 [3ln (6t) -1]

Q: Evaluate S. So dy 0 dx √√[y(1+x²)]

A: Problem is solved using concept of integral.

Q: S dy S f(x, y)dx

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Q: dy If y = (In x) (sin x), then dx

A: y=ln x(sin x) To find dydx

Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: Find d^2y/dx^2.  x=4sin(t), y=5cos(t), 0<t<2*pi d2y/dx^2 = For which values of t is the curve…

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Q: dy Find for the following function. dx 3 - cos X y = 4 + coS X dy dx II

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Q: If u- f(x) where y=J x+y%*34 show thal do

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Q: dy Find for the following function. dx y = 2x cos x sin x dy dx II

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Q: of and dy For the function f(x.y) = sin (2x - 5y), find dx of of

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Q: Find dy of the following functions or relations. dx а) In y" = x² – 4y°

A: Given :…

Q: dy Suppose y = In (2x2), where x and y are functions of t. If = 6 and x :3, find dx dt •

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Q: , find dy/dx. х • 7x² V2 + cos³t dt 126. y 125. y = V2 + cos³t dt 128. y 127. y = dt 12 + 1 dt 3 + A

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: dy (a) Find if y = (In x)=². dx

A: For (a), dydx=lnxx2'       =ex2lnlnx'        =ex2lnlnxx2lnlnx'        =ex2lnlnx2xlnlnx+xlnx…

Q: dy Inx Find if y = .2 dx

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Q: dy If y=t+t and x= 5t+7 then at x = 17 is: dx

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Q: dy Find of the following. dx 3t X = 1+t³ 3t² y 1+t3 t + -1 |

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Q: dy Find for the following function: dx 1- y = etan'x

A: It is differentiation using chain rule.

Q: Q2. Find of y = 4x/x + V at x = 1? dx

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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.

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.