The concentration C (in milligrams per milliliter) of a drug in a patients bloodstream T hours after injection into the muscle tissue is modeled by C=7t/27+t^3 use the differentials to approximate the change in concentration when t changes from t=1 to t=1.5

Q: Use differentials to estimate the value of 7+(1.02) correct to four decimal places.

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Q: Find  dy dx by implicit differentiation. tan−1(4x2y) = x + 5xy2

A: tan−1(4x2y) = x + 5xy2 We differentiate both sides with respect to x using the product rule and…

Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

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Q: Discuss how the concept of instantaneous velocity v(t) can lead to the mathematical notion of a…

A: Topic:- application of derivatives

Q: Explain the derivatives and integration.

A: Solution: Derivatives: Definition of derivatives is , the rate of change of a quantity with respect…

Q: What is the instantaneous rate of change of the graph of y = = cos x when x= 2n?

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Q: Find the differential of the function y = x- sin x.

A: Given: y=x2-sinx

Q: What is the derivative of y = cos-1 (x² + 2)? %3D

A: Derivatives formula ddxcos-1x=-11-x2 ddxxn=n xn-1

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

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

Q: Use differentials to estimate the value. estimate =  exact value =

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Q: You would like to use differentials to approximate the change in BMI when weight increases from 55…

A: Given: The function represents body mass index(BMI) is  Bw,h=wh2 where, w means weight in kilograms…

Q: Find the rate of change of y with respect to x at the indicated value of x. sin(x) :- 11 - cos(x)' y…

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Q: Use negative differential to obtain an equation of tangent curves at a given point.

A: Solve the following

Q: What is the derivative of cosh-1(xy) + elog x = sec3(y2)

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Q: use differentials to approximate the change in y if x changes from 25 to 25.3

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Q: find the first order derivative of y=sin 0.5√x/x at x=8, h=0.2 a. Forward difference B. Backward…

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Q: a- y= (cosx) (use logarithm differential)

A: To find dy/dx

Q: Calculate the derivative. 1 y = log 5x y' =0

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Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)3

A: First I have find the linearization of x^3 near x=2 and then find the required approximated value.…

Q: Use a linear approximation (or differentials) to estimate the given number. (8.09)2/3

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Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)5

A: Given term is (1.999)5Let x = 1.999

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

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Q: 2. Find the derivative of: (a) A(x) = [ 1n | In(sin(3t)) dt (b) A(x) = L, In(sin(3t)) dt

A: According to the Leibinitz rule :

Q: The size of a population of butterflies is given by the function. p(t)= 6000/(1+49(0.6)t) where t…

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Q: What is the derivative of y = e3 In(5 + e3)? %3D

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Q: Calculate the derivative. 3 y = log 3X y' =D

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Q: Find the second derivative of the function.

A: Given,         f(θ)=3tanθ

Q: Use linear approximation (or differentials) to estimate the given number. 3 а. V8.12

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

Q: Find and sketch an exponential equation of the form y = Ce^kx that passes through the points (0,8)…

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

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Q: -1/7 17 dx =?

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Q: Compute dy/dx, using logarithmic differentiation. Write your final answers entirely in terms of x.…

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Q: Use differentials to approximate the value of (3.01)2 + 2(0.99) – 3 in four decimal places.

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

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Q: 7) Find the average rate of change of the function A(x) = sin ( 2x - -) from x = to x =

A: A(x) = sin(2x - π/6) A(x2) = A(5π/6)          = sin(2*5π/6  - π/6)          = sin (9π/6)          =…

Q: Find the total differential.

A: w=3x+y4z-9y

Q: Find the derivative. 8 + e y = In 8 + et 8 - ex.

A: Given,          y=ln8+ex8-ex

Q: Find the derivative of the function. f(x) = In(sinh(x)) %3D f '(x) = %3D

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Q: A total cost function (in dollars) is given by C(x) = 116 + 3x + 0.37x. Use differentials to…

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Q: What do the differentials of x and y mean?

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Q: Determine the instantaneous rate of change of the function √ sin sin (2³) f(x) = [x² x3 At x=1 dt…

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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: (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: 1. Find the derivative of g(x): Int dt 1+t Cos

A: This will solve by Leibnitz theorem

Q: Use a linear approximation (or differentials) to estimate v3.99 to 5 decimal places. Be sure to show…

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Q: Find the derivative of s(*) - L Int dt 1+t

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Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

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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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