There is a bacteria cell in a Petri dish that is reproducing at a rate of              r(t) = 2t^2+1 per hour for 5 hours, where r is the reproduction rate in thousands of cells and t is the time in hours.  What are the domain and range of the function that describes the reproduction rate?

Q: Solve for the derivative of the function using chain rule. 4. f(x)= (x3+4)5/ 3x4-2

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Q: Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Given f(x)=(1+2x2)(x-x2) By Product rule,…

Q: Estimate the slope of the tangent line to f(x) = tax(x) at the point x = 9π/4

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Q: What is the derivative of the function f(x) = 2x + 3 at the number x = 4?

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Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Find the derivative of ƒ (x) = /7– 8x. %3D To enter va, type sqrt(a). f' (2) =

A: We have to find the derivative of the given function.

Q: Find derivative of 2x^4y^3-xy^2 using chain rule.

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Q: Evaluate the second derivative at this critical number.

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Q: C20+3xHo

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Q: # Find the derivative of frz)- (2-2)"

A: Given function is fz=z-25z2+iz+12

Q: Please show step-by-step solution!

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Q: Find the second derivative of the funcion. y%3D

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Q: 2. If the derivative of an accurately determined function is replaced with a finite difference, how…

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: 5 Find the derivative of f (x) = (9x4 -

A: Consider the given: fx=9x4−7x5Find the derivative:f'x=ddx9x4−7x5

Q: f(x) = 6x3 - 9x + 4 +4

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Q: 6. у3 2x – Jx² – 1

A: Given function y=12x-x2-1 we want to derivative of given function with respect to x

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - -2, and the line 4…

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Q: ction defined by f(x) = x2 – 3x + 4 at (-1, 2). Write

A: we have to find the slope of the line tangent to the graph of the function defined by  f(x) = x2 –…

Q: The number of licensed drivers in a country (in millions) can be approximated by the function g(x) =…

A: Here, the given function is: g(x)=178.277x0.065 where x is the number of years and g(x) is the…

Q: Compute the derivative of the function f(x) = 5x² + 3x at the point x = 4. %3D (Give your answer as…

A: We have to find the derivative at that point

Q: What is the slope of the tangent line to the graph of f(x) = x² - 3x +1 at the point (-1,5)?

A: Given: fx=x2-3x+1 To Find: The slope of the tangent line to the graph of the given function at the…

Q: 5, i, Evaluate the first and second derivatives of the function z-2x4+3x3+2x-5 when x = 4.

A: We have to find the first and second derivative of the function z=2x4+3x3+2x-5 when x=4.

Q: The second derivative of f(x) = ex²-8 is %3D Font Sizes

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Q: Use definition to find the derivative of the function f (x) = 5x- 2x at = 3. [2 Marks] %3D

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Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: 2. у %3D 3 + 4x — х?

A: We can find the answer as below

Q: Find the equation of a tangent line to the graph of f(x) = x² – 2X at (-2,8). TYPE IN THE EQUATION…

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Q: What is the second derivative of the function:  f(x) = (9x^2)/ (x^2-49) Please show ALL steps

A: Given function is

Q: se the General Power Rule to find the derivative of the f y = 124x2 + 5

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Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

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Q: Estimate the derivative of the function f (x) = -3 at the point a = 3. %3D

A: Here given as fx=x3-3 Differentiate with respect to x f'x=ddxx3-3=ddxx3-ddx3=13

Q: 3. Tak-gu baked 10 loaves of bread in 1 hour. After that, he baked a dozen of bread in 80 minutes…

A: We have three points,  A = (60 min, 10 )  B = (80 min, 12 )  C = (90 min, 12)    Hence, we have…

Q: Compute the derivative f(x)= cubed root of x + 3/x5

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Q: Find the derivative of f(x) = (2x^2-x-1)(sqrt of x) %3D

A: A detailed solution is given below.

Q: Find the derivative off (x) = 9x - 5 at x = 2 and x = 5.

A: Given f (x) = 9x - 5

Q: What is the derivative of a function f(x) = 4x³ – 3x2 at a number a? %3D

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Q: Find the first derivative by applying the appropriate rules. DO NOT SIMPLIFY the algebra. (a) fx)…

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Q: Use definition to find the derivative of the function f(x)= 2x-3x2 at x = 3 %3D

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Q: Find the derivative of the function at Po in the direction of A. f(xу) 3 - ху- Зу?, Po(-7,0),…

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Q: In(X+ bnx) %3D

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Q: Find the derivative of the function without using the Quotient Rule. 4x -27 y' = ( 4x10)

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Q: What is the derivative of y=(1-x-1)-1  Please show steps. Thanks.

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Q: Find the points on the graph of f(x)=48x−x3 where the tangent line is horizontal.

A: Given:f(x) = 48x – x3.Compute the derivative of the function f(x) as follows.

Q: Determine the line tangent to f(x) = 2x2 + 3x + 1 at (-2, 3).

A: The tangent line to a curve at a given point is the line which intersects the curve at the point and…

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: 2. Use the definition of the derivative to find f'(7) if f(x) = 4 + 3x – 2x.

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Q: FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5- x2 AT (3,–4). %3D

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Q: Find the derivative of the function at Po in the direction of A. txу) - - ху + у, Р,(10, - 2),…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.