3. fox =V X at X T6

Q: The tangent line to the graph of y=f(x)at the point (1,11) has the equation y=3x+8 (a) Find f′(1)…

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Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: 9. State the Second Derivative Test for functions of two variables z = f(x, y)

A:

Q: Q2 Use the chain rule to find the derivative of dw w = x2 + y2 with respect to t ). with x = cost -…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Suppose that a company can produce 12000 units when the number of hours of skilled labor y and…

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Q: When a vertical beam of light passes through a transparent medium, the reason that its intensity I…

A: We have to find What is the beam intensity at 15 feet below the surface.

Q: Find the 1st derivative: Complete Solution.  y=2cos2 t/2

A: y=2cos2 t/2

Q: Find the derivative gx) = 4 K) = cost dt

A: Problem is solved using Leibniz rule

Q: What is the average rate of change of y = cos (2x) on the interval [0,π/2]

A: Given f(x)= y=cos (2x) to find the average rate of change over the interval (0,pi/2) average rate of…

Q: Find the maximum rate of change of the function f(x,y) = sin (xy) at the point (4,0) and the…

A: The given function is f(x,y)=sin (xy) and the point is (4,0)=(a, b). to find : Maximum rate of…

Q: 7) Find the instantaneous rate of change of f(x) = ecos(z") + sin(In(8²)) at x = 1.

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Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

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Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

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Q: Q.2 Find the derivative at each critical point and determine the local extreme value. (a) y=x√√4x² 1…

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Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: (a) Find the derivative of fix. y. 2) = x-xy-z at P1, 1,0) in the direction of v = 2i- 3j + 6k. (b)…

A: The directional derivative of a function f(x,y,z) at the point (x,y,z) in the direction of vector v…

Q: what is the second derivative of y(t)=e^-2t and y(t)=e^-3t

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Q: Q2// A) Derivative following functions by using chain rule m 1) y = Vu, 2) y = 4u, -Va+1 Vx+1

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Q: A point moves along the parabola y = x² in such a way that the rate of change of x : kx, || dx dt…

A: Since dx/dt = 10 at x = 5, therefore 10 = 5k k = 2 Now, calculate dx/dt at x = 7. dx/dt|x=7 = 2*7 =…

Q: What is the instantaneous rate of change of f(x) = V +2-3 at %3D x = -2?

A:

Q: 5. Find the rate of change of the distance D between the origin and a moving point on the graph dx…

A: Given: y=x2+7 then A moving point on the graph is: (x,y)=(x,x2+7) And dxdt=8 cm/sec We have to find…

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: Given,   x2+y2=45To find dydt, when dxdt=-2 and x=3

Q: 5. First compute the derivative of f(x)= Vĩ and then use it to: a. Find the equation of the tangent…

A: Given equation of curve is fx=x. Power rule of differentiation states that: ddxxn=nxn-1…

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

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Q: Q:1 Find the second derivative of f(x) = 2x5 - 3VX7 at x = 1 rounded to five decimal places.

A: To find the second derivative of  f(x)=2x⁵-3x7/3 at x=1

Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: Suppose y = f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

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Q: The average rate of change of the function y = x² in the interval 2 sx< 5 is %3D

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Q: What is the approximate value of the first derivative of S(x)=-0.1x*-0. 15x-0.5x-0.25x-1. 2 at…

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Q: Determine the instantaneous rate of change of the function f(x) = [x² si sin (2¹) 1+√t x3 At x=1 dt

A:

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: The number of hours of skilled labor is y and unskilled labor is x.

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: If f(x) = cos(2x), which of the equations below describes the average rate of change of f(x) over…

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Q: (a) By using the chain rule and the derivative if x>0 (1, -1, if x< O' d (\xl) = dx | d find - (lx3…

A: Just break the mod function in two parts and easily calculate the derivative.

Q: 2. Approximate the derivative of f(x) forward, backward, and central difference method and step size…

A: To obtain the derivative at the point x0,y0, the following methods can be used:- The forward…

Q: find derivative  1. y = ln (3ue^-u)    2. y = ln (2e-^t sin t)  3. y = e^sin t (ln t2 + 1)

A: find derivative

Q: 1 By considering the secant through the points where x = 1.2 and x = instantaneous rate of change of…

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Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

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Q: Assume that all variables are implicit functions of time t. Find the indicated rate. x2 + 8y2 = 33,…

A: Explanation of the answer is as follows

Q: Consider the function Y3x2-6×+ス a. Find the slope of the tangent lihe to the curve at x=2 be Find…

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Q: . Use a similar procedure to estimate the instantaneous rate of change of y = 3" at r = 0. Show your…

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Q: 9. Consider the interval [0, 2n] for the function y sec x. State an x- value at which the…

A: Given query is to find value of x for different conditions for instantaneous rate of change.

Q: Let m(x) be the slope of the tangent line to the curve y = 2x° – 6x² + 3x at the point (x, y). Find…

A: We have to find instantaneous rate of change of m(x) at point (2,-2)

Q: (4)The instantaneous rate of change of f(r) = e- at a = 1 is . .. (5) The derivative of f(x) = sec2…

A: (4) We have So we get the instantaneous rate of change of the function at  as .

Q: 8. Find the derivative of the function (t)= 3sin(arccost)

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Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

A: