Find the first derivative of y = (x – 1) √ (2x – x2) + arcsin (x – 1), and y = arctan [ (3 sin x) / (4 + 5 cos x) ], and y = ( ex – e –x ) / (ex + e –x ) Simplify the answer but make the solution detailed and clear.

Find the first derivative of y = (x – 1) √ (2x – x2) + arcsin (x – 1), and y = arctan [ (3 sin x) / (4 + 5 cos x) ], and y = ( ex – e –x ) / (ex + e –x ) Simplify the answer but make the solution detailed and clear.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.3: Implicit Differentiation

Problem 43E

See similar textbooks

Related questions

Q: Find the length and direction (when defined) of u xv and vxu. u= 3i, v=5j The length of uxv is (Type…

Q: The count in a bacteria culture was 600 after 20 minutes and 1500 after 35 minutes. Assuming the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (31) Use Newton's Method to make the second approximation r2 to the solution of 2e = ex. Take x1 =…

A: Leibnitz Rule of differentiation: ddx∫α(x)β(x) f(x,t) dt = ∫α(x)β(x) d(f(x,t))dx dt +dβxdx f(x,βx)…

Q: Write an equation for the polynomial graphed below 5+ 4+ 3- -2- -3 -4 -5+ y(x) %3D 2)

A: topic- polynomials

Q: Find dy/dx by Implicit differentlation. x = 7 In(y- 24), (0, 5) Ap dx Find the slope of the graph at…

A: implicit derivative dydx of equation x=7lny2-24

Q: Part 1: A derivative computation using the chain rule Suppose F(x) is a differentiable function for…

Q: Verify that the given functions are linearly independent by evaluating the Wronskian at x = 0. {e2a…

Q: Solve 8 cos(2a) = 8 sin (a) + 3 for all solutions 0 < a < 2t Give your answers accurate to at least…

A: The given equation,8cos2α=8sin2α+3

Q: rcos(x) V1- t2dt d (32) Find the derivative: dx 1

Q: 4-x 16-x²-y2 Fx*+y° dzdy dx

Q: Using the method of undetermined coefficients, what is the modified form for a particular solution y…

Q: Supply the missing integrand and the limits of integration - 2sin 0 r cos?0 dr d0 = _d®

Q: The function s(t) describes the motion of a partide along a line. s(t) = t- 14t + 21 (a) Find the…

A: (a) vt=dsdt =dt2-14t+21dt v(t)=2t-14 (b) Positive direction denotes, v(t)>0 ⇒2t-14>0…

Q: Find the area of the surface obtained by rotating the curve x = /16 – y², 0 <y<2, about the y- axis.…

Q: Find the Rlemann sum for f(x) = x +3x over the Interval [0, 8] (see figure), where %3D X, = 0, x, =…

Q: Find the absolute extreme values of the function on the interval. 13) f(x) = 7x8/3, -27 sxs 8 A)…

Q: Change the following polar equation to rectangular form. Show work. 14. r = 3+sine

A: Explained below

Q: Find dy/dx by implicit differentiation. 6) x3 + 3x2y + y3 = 8 dy A) dx x2 + 3xy B) dy dx x2 + 3xy x2…

Q: Find dy/dx by Implicit differentiation. x = 7 In(y-24), (0, 5) dy %3D dx Find the slope of the graph…

Q: Suppose f(x) is a function that satisfies the following inequality for all x: 1+3 cos(x) < f(x) <…

A: Solution: The given inequality is

Q: 1. For the right triangle pictured below, find the exact values of each of the following (no…

Q: Convert to a rectangular coon 12. (3,*)

Q: 10) у - еx3 In x

Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of the Norman…

Q: 1. 3 4 27 + 13 81 243 729 The sum +7+ 10 written in sigma notation is equal to + + 16 19 22 7 3k A E…

Q: 4t + 98.6, where T is the temperature, in degrees Fahrenheit, at time t, in hours. 2+1 AT(t) 102+…

Q: wa?y+ xy² + tan (wx) Determine dyðwdx Your answer

A: solution

Q: Find dx e+5 For the toolbar, oress AL TaE10 (0g

Q: d Cos(2) (32) Find the derivative: dx V1 – t?dt

Q: Inx 1 13. lim, X X,

Q: A car starts from rest at time t 0 and accelerates with acceleration a(t) = –0.6t + 4-meters sec^2…

A: Here, a(t)=-0.6t+4⇒v(t)=∫a(t) dt⇒v(t)=∫-0.6t+4dt⇒v(t)=-0.3t2+4t is the velocity function.

Q: Evaluate the definite integral. es dx x/ln x v 5 6568542194924

Q: 11. Given the functions: g(x) = tn(4 – x) and h(x) = 4 – x² find and simplify the following: (a) h(x…

Q: When 20 N of force is applied to a spring of natural length 2 m, the resulting compression is 0.5 m.…

Q: Evaluate the following integral: 10x dx O 2

A: Integration

Q: +2D+2)y = e csc x

A: Solution: (D2 +2D +2)y = e-xcsc(x)

Q: Converting 1530 degrees to radians will correspond to which value? 19n 3 201 B 3 29Tt

A: The value of θ° to radians is given by ∅ = θ×π180 radians

Q: lim - Evaluate the given limits using L'Hôpital's rule/Squeeze theorem: 1 lim X→0+ ех-1, 1 lim x cos…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first question. If you…

Q: (28) A particle is moving in a straight horizontal line. Its position, s(t), velocity, v(t) and ac-…

Q: 3. S sin x In(cos x) dx

A: According to company rule, we can answer only first question.

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

Q: Find dy/dx by implicit differentiation. 8x3 + 9y3 = 66 dy/dx =

Q: -4x Calculate the following integral Je dæ by using a substitution O - 0.25e^(-4x) + C O 0.25…

A: ∫ e-4xdx

Q: Inx Evaluate the integral (show clear work!): S dx

A: SOLUTION-

Q: Find each limit, If it exists. 6- 4x (a) lim 6x - 7 4x (b) lim * 6x-7 () lim 6x 6-4x2 %3D Submit…

Q: Use the law of cosines to determine the length x in each figure. Leave your answers in terms of…

Q: To find the distance across a small lake, a surveyor has taken the measurements shown. Find the…

Q: The point P(48, –14) is on the terminal side of angle e in standard position. What is the value of…

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

Q: Find the Rolle's theorem For the Following function and iFit is truerfindthe Value oF C

Question

Find the first derivative of y = (x – 1) √ (2x – x²) + arcsin (x – 1), and y = arctan [ (3 sin x) / (4 + 5 cos x) ], and y = ( e^x – e ^–x) / (e^x + e ^–x)

Simplify the answer but make the solution detailed and clear.

Expert Solution