Find the relative rate of change, f'(t) of the function f(t) = 3e2t. f(t)’ f'(t)

Q: What is the rate of change of y = ln x at x = 10?

A: To find the rate of change we have to find dy/dx

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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: Find the derivative of the function f(x,y) = x +xy + y at the point (- 2,- 1) in the direction in…

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Q: 5. Second derivative of y = 1+t)< t2

A: Given: y = 1+t2t2 To find: Second derivative of the given function.

Q: Find the derivative of y with respect to x for y = 7*. dy dx II

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Q: Find the average rate of change of f(x)=x² – 5x from: x, =-1 to x, = 3

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

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

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Q: Find the derivative of y with respect to x. Y=ln(13x)+x dy/dx

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Q: Approximate the derivative of y=x at x=1 by forming small changes.

A: SOLUTION:-

Q: Find the derivative of the function f(x) = ln(sinh x)

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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: Let f:[-n, 7] –→ R, where f(x) = 2 sin (2x) – 1. TC Calculate the average rate of change of f…

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Q: Find the average rate of change of f from 0 toπ/2 . f(x)=sin( x/2)

A: Derivative of a function determines the change of one variable with respect to another variable.…

Q: Find the derivative of the function.

A: we have to find the derivative of the function F(x)=∫1x1+t4dt

Q: Find the derivative of the function. f(z) = V - VE f '(x) =

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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: 4y4 at the Find the maximum rate of change of the function f(x, y) point (5,1)

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Q: What is the average rate of change of y with respect to over the interval [-1, 2] for the function y…

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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: Find the derivative of the function f(x, y) = e³ at the point (0, 2) in the direction in which the…

A: The derivative of function f(x,y) can be determined by the gradient of the function,…

Q: Find the derivative of y = x4 sinh(z). dy/dx =

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Q: Calculate the second derivative y : Vx - Vy = 1

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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: Find the derivative of the function. y = ex ln x

A: Consider the following equation: y=exlnx Differentiate y with respect to x: dydx=ddxexlnx Apply the…

Q: The average rate of change of the function y = sinx over the interval [0, ]is 4

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Q: Find the derivative of y with respect to x. Y=ln(13/x) dy/dx

A: Given, y=ln13x we have to find derivative of y with respect to x.

Q: y = x+1 y = sin v1+x?

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: Find the instantaneous rate of change of y =- at x = a

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Q: What is the first-order derivative of y = x^y?

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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: 1. Find the derivative of the function:F(x)= [ (Vt arctan t)dt .

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Q: (d) Compute the driectional derivative of f at (1,2) in the direc- tion u = (e) • point (1, 2)? What…

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Q: Find the derivative of the function. y = 5 e - 5x+1 dy dx

A: Note:- Answer is given in the picture

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

A: First find gradient and take magnitude for max rate of change

Q: Which is the first derivative of y=vx ?

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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: Find the derivative of g(x) = fecost dt.

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Q: Find the derivative of the function. y = log |5- 2x dy dx

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Q: Find the derivative of the function. 1 g(x) = dt Jtan(x) V2 +

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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: Approximate the derivative of y=x² at x=1 by forming small changes

A: We have to find the derivative of the function y=x2 at x = 1 by forming the small changes.

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: Can you help me with this problem step by step?

A: To determine the first derivative of the function.

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

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Q: Which is the first derivative of y=vx ? *

A: Given Data: y=x Formula: d(xn)dx=nxn-1

Q: Find the average rate of change of the function f(x) = x 5x - 1, over the interval [-1,3

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