(c) Let 2t h(t) = / 22 d.x. Use the Fundamental Theorem of Calculus and the chain rule to find h'(t). If h(t) represents the position of a moving car at time t, calculate the velocity of the car at time t = 0. %3D

Q: Let y = 5√√x. Find the change in y, Ay when x = 1 and Ax = 0.3 Find the differential dy when x = 1…

A: It is provided that y=5x. We need to determine ∆y for x=4, ∆x=0.3 and we need to determine dy for…

Q: Let y = 2x2. Find the change in y, Ay when x = 5 and Ax 0.1 Find the differential dy when x = 5 and…

A: We have to solve

Q: Let y = 2/x. Find the change in y, Ay when x = 5 and Ax = 0.1 %3D Find the differential dy when x =…

A:

Q: 18. y = x/I - x?

A: Differentiation:- The derivative of a function of real variable measures the sensitivity to change…

Q: Find the differential dy of the given function. y = V4 - x2 dy =

A:

Q: Let y = 5a2. Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4…

A: ∆y = 5(x + ∆x)^2 - 5x^2= 5(x^2 + 2x∆x + ∆x^2) - 5x^2= 5(2x∆x + ∆x^2)= 10x∆x + 5∆x^2 So when x = 4…

Q: Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t = 0

A:

Q: Let y=(x^2+2)^3 Find the differential dy when x=2 and dx=0.5  Find the differential dy when x=2…

A: Given:

Q: Let y = 5a. Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4 and…

A: According to question given y=5x2x=4 and ∆x=0.4We have to calculate the change in y, ∆y

Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

A:

Q: Let y = 2/x. Find the change in y, Ay when x = 3 and Ax = 0.3 Find the differential dy when x = 3…

A:

Q: Let y=5x2y=5x2.Find the change in y, Δy when x=3 and Δx=0.2   Find the differential dy when x=3 and…

A:

Q: Q9/ use the chain rule to express dy/dx in terms of x and y and choose correct answer. 1 x = t2 at t…

A:

Q: Let y=e^(x/2).Find the differential dy when x=1 and dx=0.3 Find the differential dy when x=1 and…

A: Given function is The differential dy is evaluated as follows,

Q: Let y = 3x2. Find the change in y, Ay when x = 2 and Ar 0.2 Find the differential dy when x = 2 and…

A: We have to find solution

Q: Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t=0

A:

Q: Let y = 4/T. Find the change in y, Ay when a 3 and Ar Find the differential dy when x 3 and dx 0.2

A: fx=4x here x=3 f3=43 . Δx=0.2 fx+Δx=4x+Δx f3+0.2=43+0.2 f3.2=43.2 . Δy=f3.2-f3 Δy=43.2-43…

Q: Let y = 2 T. Find the change in y, Ay when x = 1 and Ax 0.2 0.190 Find the differential dy when x =…

A: please see the explanation below

Q: Let y = (x² + 3)5. %3D Find the differential dy when x = 5 and dæ 0.4 Find the differential dy when…

A:

Q: Let y = 5 x. %3D Find the change in y, Ay when a = 5 and Ax = 0.3 %3D Find the differential dy when…

A:

Q: Let y = 4x. %3D Find the change in y, Ay when x = 5 and Ar = 0.4 Find the differential dy when x = 5…

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

Q: Let y = (x² + 2)4. Find the differential dy when x = 1 and dx = 0.1 Find the differential dy when x…

A:

Q: Find the differential dy of the given function. y = (x + 1)/(2x − 1)

A:

Q: Let y = 5x?. Find the change in y, Ay when a = 3 and Ax = 0.3 Find the differential dy when x = 3…

A:

Q: If y approximate the differential dy when x changes from 64 to 64.07

A:

Q: Let y = 4x“. Find the change in y, Ay when x = 3 and Ax Find the differential dy when x = 3 and dæ =…

A: Given that: y=4x2, x=3 and ∆x=0.4

Q: dw Use the Chain Rule to find dt w = x²e²y cos(32), x = cos t, y = In (t + 2), z = t

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x).

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A:

Q: Let y = tan(3r + 4). Find the differential dy when T = 4 and da 0.4 Find the differential dy when x…

A: Given: Differentiate the above expression of 'y' with respect to 'x'.

Q: Let y = e/3 Find the differential dy when x = 5 and dx 0.2 Find the differential dy when x 5 and dx…

A:

Q: Suppose y = (x² + 5)³. (a) Find the differential: dy dx. (b) Compute the differential when x dx 2…

A:

Q: Let y = 5,a. %3D Find the change in y, Ay when r = 5 and Ar = 0.2 Find the differential dy when r =…

A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…

Q: Q4) Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t = 0

A:

Q: Let y = (x² + 1)². Find the differential dy when x = 5 and dæ = 0.5 Find the differential dy when x…

A: Consider the given function as y=x2+12

Q: Let y = 4/r. Find the change in y, Ay when x = 3 and Ax 0.2 Find the differential dy when x= 3 and…

A: We know that, Δy= y(x+Δx)-y(x) Given, y= 4√x --------equation 1 x=3 Δx= 0.2 Therefore, Δy=…

Q: Let y = (x2 + 2)2. Find the differential dy when x = 4 and dx = 0.1 Find the differential dy when x…

A:

Q: Let y=(x^2+2)^2 Find the differential dy when x =5 and dx =0.5 Find the differential dy when x=5 and…

A: a) Find dy for given equation.

Q: Find the differential dy of the given function. y = V4 - x2 dy

A: Consider the given function. The problem requires to find the differential dy of the given…

Q: Let y 3T. Find the change in y, Ay when x 2 and Ax 0.3 Find the differential dy when a 2 and da 0.3

A:

Q: Let y = 3x². Find the change in y, Ay Ay when x when x = = 5 and Ax = 0.3 Find the differential dy…

A: Given f(x)= 3x2

Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Let y = 3a. Find the change in y, Ay when x = 1 and Ax = 0.4 Find the differential dy when x = 1 and…

A: Given that: y=3x       NOTE: As per our answering guidelines, we can only answer 1 question or 3…

Q: Let y = 4/T. Find the change in y, Ay when x = 4 and Ax = 0.1 Find the differential dy when x = 4…

A: Given:- f(x) =4√x To find :- Change in y , Δ y when x = 4 and  Δ x=0.1  Differential dy when x= 4,…

Q: Let y = 4ĩ. Find the change in y, Ay when x = 4 and Ax = 0.3 Find the differential dy when x = 4 and…

A:

Q: Let y = 2x2. Find the change in y, Ay when x = 1 and Ax = 0.1 Find the differential dy when x = 1…

A: Given function is y=2x2, The change in y at x=1 is given by,…

Q: Let y = 2x². Find the change in y, Ay when x = 4 and Ax = 0.2 Find the differential dy when x = 4…

A: It is provided that y=2x2. We need to determine ∆y for x=4, ∆x=0.2 and We need to determine dy for…

Q: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx)  y = (2 x3 − x2…

A:

Q: Let y = 3x². Find the change in y, Ay when x = 1 and Ax 0.1 Find the differential dy when x = = 1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…