Consider a continuous function y=f(X) whose first derivative is y'=x(x-2)

Q: gives the first derivative of a continuousfunction y = ƒ(x). Find y″ and then use Steps 2–4 of the…

A: Given that the first derivative of the function is  y'=(8x-5x2)(4-x)2

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: The solution for the above question is as shown below.

Q: Find a function with derivative equal to g(x) = cos(x)e³sin(x)

A: To find a function with derivative equal to gx=cosx e5 sinx

Q: 3) Find the second derivative of y with reference to x. xcosy = y

A:

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

A:

Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec = sec-1 27) y = -sin-1 (5x2 + 2) 28)…

A:

Q: Find y' by implicit differentiation 1. x²+4x-3y²+4y=0 2. 2xy+π sin y = 2π

A:

Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

A:

Q: Find the derivative of y = 3x ln (x)? A. Y = 3(1+ ln (x)) B. Y = 3 + In (x) C. y = 1+3 ln (x) D. Y =…

A:

Q: 4. Consider the function f(x) = 2 cos x x2 find its derivative

A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2

Q: ind the derivative of y=(x-1)(2x-x2)1/2 - arccos(x-1)

A: Given function: y=x-12x-x2-arccosx-1

Q: 2. Find the derivative of y= ecos{/x+3) Solution:

A: Topic:- derivatives Note:- as per our guideline if more than one question uploaded than only first…

Q: Determine the first derivative of the ff. function a. y = 400(2)**3 sin 3x b. y = Vxe2* cos x…

A:

Q: 6. Use implicit differentiation to find first order partial derivatives: tan-(x²y) = y²z3 +…

A:

Q: Find the derivative of y = 4) G* eln sin-) y = G (In-x) sin + V4 – x2. x sin¬1 In sin + (Tx-1 1 y' =…

A:

Q: 6 Find the derivative of f (y) =7tan(y) - 6.

A:

Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…

A: To find the extreme points.

Q: C. Find the derivative of each function. x' - 2x 3. h(x) = 4. F(x)=sin x- cos x- tan x tan x D.…

A: Follow next step

Q: 6 Find the 3rd derivative of y = (x-1)2

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find the derivative of y with respect to x. y = csc-1(x5 + 1) ; x > 0

A:

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: 4. Find and classify the critical points of the given function by using Second Derivatives Test. 1 1…

A:

Q: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

A:

Q: (3e)® arctan (3x³) In(e2«) arccos(5x) 1. Find the derivative of f (x)

A:

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

A: Given,

Q: 6. Find the derivative of function. a) y = (x - 1)ā + 2x2-4x+7 b) y = cos* 3x * arcsin 3x2 |3D 3 c)…

A:

Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

A:

Q: 1) Find the derivative. Simplify where possible. y = x tanh-1x + In/1 – x²

A:

Q: find derivative  1. y = ln (3ue^-u)    2. y = ln (2e-^t sin t)  3. y = e^sin t (ln t2 + 1)

A: find derivative

Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: 1) Find the derivative of f(x) 1+sin 2 x %3D 2 cos x

A: we are given the function is  f(x)=1+sin2x2cos3x

Q: (2) Find the derivative of the following: y = xsinx + x² y = (x² + 1)** + sin(x*)+ x* 2. 3. Iny = e'…

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: 1) Find the 3rd derivative of y = sin(x) %3D

A: To find the 3rd derivative of y=sinxx. Solution: For finding third derivative, we need to find first…

Q: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

Q: Solve for the derivative of the Inverse Hyperbolic Differentiation. 1. y = sin h-1 (2x2 - 1) 2. y…

A:

Q: 1. Find the first order derivative of u = x*.

A:

Q: 3. F(x) = " In(x) (4t + et) dt. Find the derivative of F(x).

A: Given, F(x)=∫1ln(x)(4t+et)dt To find : Derivative of F(x) By using the second fundamental theorem of…

Q: 2) Use the chain rule. (Chapter 2.5) Find the derivative y= (x² +3x)*

A:

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: (a) Show that the derivative solution of this function y = x** is x(x*+x-1) [1+x In x (In x + 1)] dx

A:

Q: 31. Using one-sided derivatives, show that the function f(x) = {2. [x² +x, | 3х — 2, х> 1 does not…

A: Given: fx=x2+x     , x≤13x-2   ,  x>1

Q: can you help me step by step with this problem?

A: Let z= 6x^2+1 Substitute that. Then take d/dx on both sides.

Q: Find y'' by implicit differentiation. x2 + 4y2 = 4 y'' =

A: The detailed solution is as follows below:

Q: 5. Find by implicit differentiation for x + y = xy. dx

A:

Q: 1) Find the derivative of the function: (3х — 1)3 Vx* — 1 f(x) = cos² x

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. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

A:

Q: ■ Find y 2    implicit differentiation.   x4 + y 4= a4

A: Givenx4 + y4 = a4differentiate with respect to x4x3 + 4y3 dydx = 0dydx = -x3y3 — 1Differentiate with…

Q: Example2: Find the derivative of w=xy+z if x=cos t ,y=sin t &z=2t?

A: