A particle moves along the x-axis with velocity dx/dt = ƒ(x). Show that the particle’s acceleration is ƒ(x)ƒ'(x).

Q: Compute the derivative of the function F (x) = L evi dt.

A:

Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

A:

Q: Show that if acceleration is constant, then the change in velocity isproportional to the length of…

A: Show that if acceleration is constant, then the change in velocity is proportional to the length of…

Q: A particle moves along the curve y = x^(3/2) in the first quadrant in such a way that its distance…

A: Let (x,y) is a point on y = x^(3/2)Distance of (x,y) from (0,0) is given by:

Q: Find the anti-derivatives, using ONLY basic rules + 3* ) dx

A: Note:- We’ll answer the first question since we answer only one question at a time. Please submit a…

Q: Use linear approximation or differentials to estimate the following

A: Solution: Consider the given number: 1000.033 Let y = x3 = x13 Differentiating with respect to x:…

Q: If the acceleration of a particle is given by ä = sint i+ cost +e k, find the relity and position…

A: The acceleration of a particle is…

Q: Calculate dy/dx using implicit differentiation. 3x + 4y3 = 7

A: 3x + 4y3 = 7 We need to find the derivative using implicit differentiation.

Q: Use differentials to approximate the quantity   √17

A:

Q: Find the derivative of y = = Ve-5t +1 dy dt ||

A:

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: Compute the derivative: 3 | Vsin t dt dx

A: To find ddx∫x3sin t dt We know that, ddx∫u(x)v(x)f(t) dt = f(v(x))v'(x)-f(u(x))u'(x) Then, we have,…

Q: Determine the anti-derivative of Y = 2e3x +5 and use the fact that y(0) = 7 to %3D dx determine c,…

A: We first separate the variables and then integrate  c= integrating constant Formula used:

Q: Find the derivative of the funciton F(x) = ,5t dt. F'(x) =

A:

Q: I need help with this question

A:

Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

Q: Calculate the derivative: + (2t3 – 9t) dt = dz

A: Evaluate the given derivative as follows. ddx∫0x2t3-9tdt=ddx2t44-9t220x=ddx2x44-9x22-0

Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: The integrating factor of the linear DE of order one + y csc x = sin x is dx

A:

Q: calculate derivative of y wi reapect to ino dy

A: The derivative of the given function is calculated with the help of the formula d(x^n)/dx =…

Q: Calculate the derivative 10z d dz In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A:

Q: Find the derivative of the funciton F(x) = dt. F'(x) =

A:

Q: Find the set of orthogonal trajectories for r = VA sin (2e)

A:

Q: Find the derivative of the function.

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

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 Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) 5t…

A:

Q: Find the derivative of the function. -1 y = (3t – 1)(6t – 5) dy dt II

A:

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

A:

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 differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: Calculate the derivative 12x d dx In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A: follow next step

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

A:

Q: 2x f(x) sec(t*) dt. %3D -2x

A: Given,            f(x) =∫-2x2xsect4 dt

Q: A particle moves along the curve y = x3/2in the first quadrant in such a way that its distance from…

A: Let w de the distance between origin and the particle at any time t. Given that, dwdt=11 Now by…

Q: Let f(x, y) = cos(x+y²). Compute the rate of change in the direction of fastest increase for f at…

A: Find gradient and its magnitude then solve

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 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: Calculate the derivative d dz (2t5 34 dt using Part 2 of the Fundamental Theorem of Calculus.

A: The solution are next step

Q: Does the differential dy represent the change in f or the change inthe linear approximation to f ?…

A: Given the differential is dy.

Q: By differentiation with respect to time, show that the equation x = xi + ut + 1/2 at² describes…

A: Given that, x=xi+ut+12at2. Where, xi is the initial position. u is the initial speed a is the…

Q: Use a linear approximation (or differentials) to  estimate the given number.  (1.999)4

A: Consider  1.9994

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

A:

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

A:

Q: Find the derivative of g(x) = |. •r In z Vt2 +t+1 dt

A:

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y = 2 sin3…

A: We can use fundamental theorem of calculus in order to solve the given problem.

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

A:

Q: Find the derivative dy/dx of the Archimedean spiral.

A:

Q: Find the derivative of the given function a. F(x) = dt 1+ b. g(x) = [ - dt sinx 1+1*

A: