1. For the function h(x) whose graph is shown, find the values of x such that the derivative is positive, negative, zero, or undefined. y=h(x) a) h'(x) > 0 8 Answer b) h'(x) < 0 Answer 4 c) h'(x) = 0 Answer d) h'(x) is undefined 1 2 3 4 8. Answer 6, 5, 6. 2.

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: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

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Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

A: Given problem:- Find an equation of the tangent line to the curve, f(x) = 1/(x2 + 1) by using the…

Q: Find the derivative of the function. 1 - e3x = cos y = cos 1 + e3x y' =

A: Differentiate

Q: What is the derivative of x sin(x) at the point (6,5)? 2 O 1 O-1 O None of the above

A:

Q: 4) Find the derivative of the function: x* cos x h(x) %3D Vx2 + 1

A: Answer

Q: find the derivative of y with respect to xas appropriate.11. y = ln 3x + x              12. y = 1/ln…

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

Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: | If In(x² – 3y) = x – y + 3 and y(-2) = 1, find y (-2) by implicit differentiation. y(-2) = An…

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Q: 3. Solve the first derivative of f(x) = evx at x = 0.5 using centered finite-divided difference and…

A: To find the first derivative of f(x) at x=0.5 using centered finite-divided difference and a step…

Q: Find the derivative of y with respect to 0 y = 8e°(sin e - cos €) O 16e° sin e 8e (sin e - cos 0) +…

A: Given. We are given function of Y and theta and we need to find the function dY/d theta The concept…

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: Q.2 Find the derivative at each critical point and determine the local extreme value. (a) y=x√√4x² 1…

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Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

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Q: The implicit curve given by the equation x + xy + y= 1 has derivative dy 2x+ y %3D dx x + 2y Show…

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Q: Find the derivative of y = In (tanh x).

A:

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

Q: 3. The derivative of f(x) = In x at x = 3 when h = 0.002

A: 3) To find the true error and relative error of the function: f(x)=ln x, x=3 &amp; h=0.002

Q: derivative of g(x)= intergral from 1 to root x, (z^2)/z^4+1

A: ddx∫1xz2z4+1dz

Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

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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. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

A:

Q: Is it true that every function y = ƒ(x) that is differentiable on [a, b] is itself the derivative of…

A: Any function y = ƒ(x) is said to be differentiable on closed interval [a, b], it should be…

Q: 15. What is the derivative of the function: F(x) = x cos(5x) F(x) = x cos(5x) F'(x) = (x)…

A: Solving

Q: i. Show with the aid of Argand Diagram, where Ln(z³ + 3) is analytic . ii. Determine the derivative…

A: The given complex function is fz=lnz3+3.

Q: Suppose the derivative of ƒ is ƒ'(x) = x - 3.a. Find the critical points of ƒ.b. On what intervals…

A: We have to find: a. critical points of fb. On what intervals is f increasing and on what intervals…

Q: find the derivative of y with respect to the appropriatevariable. y = (θ2 + 2θ) tanh-1 (θ + 1)

A: The given function is y=θ2+2θ tanh-1θ+1. Obtain the derivative as follows.

Q: Compute the derivative of h(sin(x)) at x = assuming that h' (u)|=0,5 = 14. lu=0. Use symbolic…

A: Given:   Function : h(sin(x))    x = π/6 h'(u)| x = 0.5  = 14

Q: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

A: Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented…

Q: Compute central difference approximations for the first derivative of the function, y =[ elnx)2 , at…

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

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Q: 1 By considering the secant through the points where x = 1.2 and x = instantaneous rate of change of…

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Q: Find the first derivative of * In (sec y + tan y) - x - sinx = 2 O tany (cos.x + 1) O cos y (cos x +…

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Q: How did he get the second derivative step by step and a clear line please 3 F(x) = 1+e siny x Fex)…

A: Let fx=1+e-xsin 4x

Q: 5. What is the value of the second-order derivative of the function with parametric expression x =…

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Q: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…

A: Use the chain rule to differentiate the above given function and than use the given derivative of…

Q: 3. Find the derivative of: y = csch¬(In (sech(sec()))).

A: Note:Two questions submitted simultaneously, kindly upload question 2 separately.

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

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Q: So far, you've examined the function y = In x and its derivative, y' = , for large values of x. Now,…

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Q: Consider the function f(x) = x³ Q 2: Calculate its first derivative at point x = 3 numerically with…

A: We have given , f(x) = x3

Q: Compute the derivative of h(sin(x)) at x = * assuming that h' (u)lu=0,5 = 10. (Use symbolic notation…

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

A: This will solve by Leibnitz theorem

Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: 2- Find the derivative of y with respect to the Exercises 1-3. y = 6sinh ; 1- = - sinh (2x + 1) y =…

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Q: Show that x + yx−1 = 1 and y = x − x2 define the same curve [except that (0, 0) is not a solution of…

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Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…