dx dy =10 what is the value of Suppose x and y are functions of a third variable t. If Xy 20 and when x=22 -2 -1 2

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Q: Find 2 dr if y=1-t² and x= 4+² dx

A: 1.       dy/dt = d/dt [ 1- t²]   = -2t        2.      dx/dt  = d/dt [ 4t²]     = 8t   So now…

Q: dy 6. Find dx for each of the given functions using the sum and difference rule. b. y = ?- 2 1 a. y…

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Q: dy and d²y if x = t and y = 3. Find dx dx? 1+t 1+t

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Q: (S dx (f(+ 2t)° dt (2+3x)

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Q: dy/dx - y = xy5 = 0 Ans. 1/y* = -x++ ce 4*

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Q: dy Q:: Find for the following functions: - dx 1) у %3D (х — 3)(2х + x?)

A: Explanation of the solution is given below...

Q: dy Given y = xy² + e* calculate and report the value of when y = x = 1. dx

A: Given,  y=xy2+ex

Q: dy 5.) dx -2x +y = ye +y = ye (ye*) ³ 1 е : ²³-7e²ce Ans: y³ 3X ce ³2

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Q: dy = 3x -1 and if y= -1 when X=1, then y= If dx

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Q: dy Which is the of the equation y = e 2x+3? dx 2 В. х+ 3 С. 2х + 3 X + 3 2X + 3

A: given  y=e2x+3 find dydx

Q: d/S Vx5 dx el S- dx, (x # 0) 2x

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Q: dy 2 Find for y = Vu and u =x +3. State your answer in terms of x only. dx

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Q: C. Find the value of dx/dz&dx/dy y lnx-x² + 4 = 0 at the point (1,-1,-3) if the equation xz +

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Q: 4. x - 2 dy 26. If y = find at x = 1. 2x - 1 dx (A) -52 (В) -28 (C) 13 (D) 52

A: Find the derivative as follows: y'=ddxx3-22x5-14   =4x3-22x5-13ddxx3-22x5-1…

Q: xf (x² )dx if f(x)dx = 7. Find Enter the exact answer. f (x² )dx =

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Q: f (x) = x² + 6x if x = 2 and dx = 0.3, determine dy

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Q: find the equation of y where dy/dx = 3x + 5 and y= 6 when x = 0

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Q: dy . dx Suppose x and y are variables that satisfy the equation x – y? = 12. What is

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Q: Vx² –1 (2x +1)* 2 dy for the following function: f(x)= ln- dx Find

A: To find The derivative of the given function

Q: dy x3 + 2xy. y 7. Find for the implicitly defined function dx

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Q: dy 10. y-x dx dx

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Q: What is the value of dy/dx at x = 4 of the function? x-5 y = 2x+1

A: Given                     y=x-52x+13 we know that…

Q: Find ( d^2 y / dx^2 ) for the given function

A: 191. The given function is y=xsinx-cosx. Differentiate both sides of the above function with respect…

Q: Find dx * and then simplify whenever possible. dx2 1) y = 3t5 – 2t x = 4t3 2) y = t-3 – 7 x = t? –…

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Q: = 2-x² and f'(2) dy when x = 1. dx 8. Let y f(1+ Ju), - 3.Find

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Q: d'y 1 ,3 1 when x = 0. 3 14. Evaluate y" or of the function dx 3 || 1/3

A: Derivative of a function:           The derivative of a function y=f(x) of a variable x is a…

Q: d? V5 - 2x . dx² 9) Find 10) Find the second derivative of k(z) = 4 cs z.

A: Given, a) d2dx25-2xb)k(z)=4 cosec z To find : Above values of differentiation.

Q: Q: Find for the following functions: - dx 1. 1) y =+ 8x

A: To find the dy/dx for y=(6/√z²)+(1/8x⁴)-(1/2x⁸)

Q: dy = 8x - 7 and y(9) = 0. dx Find the function y(x) satisfying

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Q: Ex:Salve the d.fferential equation (3x-y-1)dx-(X-y+3)dy-o

A: A function f(x,y) is called a homogenous function of degree n, if it satisfies the condition…

Q: d²y and dx2 Find dy then simplify whenever possible. dx 1) y = 3t5 – 2t x = 4t3

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: dy for the following implicit functions: 9. Find dx 3Xy = (x'+ M/N

A: By using formula  of derivative

Q: dy/dx equals (xy + y^2 + x^2)/(x^2)   Considering y is a function of x, determine the solution of…

A: We need to find the solution of the above given differential equation.

Q: where a = and b = 16 10% f(x) dx = f* f(x) 10 24 [*1 (2) dz - f(2) f(x) dx

A: To find the value of a and b.

Q: dy = 4x -3 and y(4) = 0. dx Find the function y(x) satisfying

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Q: dy Q:: Find for the following functions: - dx 1- y = 2cot? `x+1

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Q: Sf(x)dx = 5.m L,(4f (x) + 2)dx. Given find

A: by integration

Q: dx 3. S x V1-4 In2x

A: follow next step

Q: dy If = 3x2 – 1, and if y= –1 when X=1, then Y= dx

A: We need to integrate the given to solve it

Q: dy Find for the following functions: dx = x 2 ³+ x4 +x -3 y =

A: Given :

Q: dy dx Suppose x and y are functions of a third variable t. If Vx+ Vy=5 and -3, what is the value of…

A: Differentiation

Q: 8. The value of dy/dx when x = -3 in the given function y = /25 – x² 1 A. 4 3 В. 4 5 С. 4 7 D. 4 9.…

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Q: (c) S (d) S: xe* ;dx (1+x)2 ex dx V1-e2x

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Q: x+6 7. y= 2 b. x3 c. + d. - 18 18 를+ 18 а. с. x3

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want…

Q: Solve

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Q: り のx + ex t 1tx - dx x* + 2x t 5

A: (i) ∫dxx=ln(x) (ii) ∫dxx2+a2=1atan-1(xa) (iii) ∫xndx=xn+1n+1, for any real number n.

Q: d'y Find the function y(x) satisfying = 30, y"(0) = 14, y'(0) = 6, and y(0) = 6 .3 dx

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Q: 1 f'(x) = 5x +1 dx

A: The given function is: f'x=5x-12+1dx f0=3 To find the value of f(4)