dy Find the value of at t = 1 if dx? Vt2 + t, y = t2 + 3 x = 4

Q: Using the fomat of dy/dx below, find (A +B+C+ D). dy 40t? + At +B dx -Ct? + Dt + 3 ||

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Q: Find dy/dx in terms of t if x=te^t , y=6t+6e^t dy/dx=

A: Use Product rule of derivative and find the derivative of x with respect to "t".

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: Using dy 3 =dx and dx = 0.03, what is dy whenx = 2? 2V3X – 2 dy i (Write as an exact decimal.)

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Q: Find dy/dx for y = J_1P+4 t2 dt t2+4 X. 3

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Q: dx x2+y?, dt dy 2, find dt dL when x = dt If L = V -5, and 7 and y = 6. dL dt

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Q: Find dy/dx and d^2y/dx^2 X=t-e^t, y= t+e^-t For which values of t. Is the curve concave upward?

A: Given that, x=t-e^t, y= t+e^-t

Q: find dy/dx for the function ex+y+2x-3y=e using implicit differentation.

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Q: Q1-lf x= cot-VE, y= , find dy dx' dx2 at t = 2. t+1

A: We have to find first order and second order derivative of the given parametric functions.

Q: Find dy/dx and d²y/dx². For which values of t is the curve concave upward?

A: x = t2 + 1 y = et - 1 dy/dx = dy/dt ÷ dx/dt

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

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Q: dy Find the value(s) of dx at y=1 given that x2y+y2 5. ony A only -클 only 3. D 2/3

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Q: dy 1. Obtain from the following. dx 3at? y = 1+t3 3at x = (a is constant) 1+t3

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Q: (c) Prove that L{Cost Si(t)- Sint Ci(t)} Logs s +1 %D

A: The complete solution is in given below

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: Find dy if x=t+6f and y= dx 2 5 at t=1 +

A: We have to find dy/dx

Q: dz The sides of the rectangle below increase in such that dt 1 and a way dx dy 3. At the instant…

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Q: dy d’y The order and degree of the DE + = 0 respectively, are and dx dx?

A: The order of a differential equation is the highest order derivative it contains. The degree of a…

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

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Q: Find dy/dx and d?y/dx2². x = t2 + 1, y = t2 + 5t (2t +5) dy dx 2t (2:(2) – (2t + 5)(2)) d²y dx2 412…

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Q: b) Find fo dy for y = Vt-1 t = sec?x sint

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Q: dy where y = coS cos (V5æ). Find dx

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Q: b) If y = sec (sint), and t = Vx + 4 find dx b) Find dx2 d²y if mx Vt2 + 5 dt + sinx = y – x secx…

A: Differentiation: Let us assume y=f(x) is a function of x. Then the rate of change of y with respect…

Q: dy Find where y = csc dx Provide your answer below: dy dx = +9). 6x + 9

A: y = csc-(1/(6x+9)) find dy/dx = ?   here we use formula  dcsc-x/dx = -1/xx2-1   using this formula…

Q: Given x = 8 In(t) and y = 64 t² then find dy %3| dx d²y %3D dx? ||

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Q: Find dx/dt. Since x + y =225, then %3D 2x dx + at 2y.dy =D0 %3D This Simplifies to dx = dt dy %3D

A: Given: x2+y2=225 To Find: dxdt

Q: Compute xe" dx + x?y dy along the curve x 3t, y = t2, 0 < t < 1.

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

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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: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: IV. Find of the following. dx = V1-t 1. ly = V1+t %3D 3t X = . 1+t3 3t? y = 1+t3 tま- 2.

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Q: dy Given that y = find . dz'

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Q: dy If y = (t + 6t + 5) (6t² + 6), find dt dy dt ||

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Q: Find dy/dt using the given values. y = x3 - 5x for x = 3, dx/dt = 4. dy dt

A: Value of dy/dt= 88 See the calculation below

Q: Find dx/dt. Uince x² + y^ = 225, then. 2x dx dt 2y.dy 24- ニ

A: Given that x2+y2=225 we have to find the value of dxdt.

Q: dy 4 Find for y dx V10 – x?

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

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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 Using the product rule for the dx function y = e3" sin x is equal to

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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: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

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

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Q: Find dy/dx if y = J' V1 + ² dt. Explain the main steps in your calculation.

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Q: =lf y = elsinx) at a point r = 1/2 then dy/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.

Q: dy Given that y = x°e", find dx dy dx

A: In this question, we need to find the derivative of y = x9ex

Q: dy Given y = vx² – 5x, evaluate using delta process. - dx

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