(a) changes from positive to negative О (-2, 3) O (1, 5) O (4, 7) O None of these points represents a change in f'(x) from positive to negative. (b) changes from negative to positive O (-2, 3) О (1, 5) O (4, 7) O None of these points represents a change in f'(x) from negative to positive. (c) does not change sign O (-2, 3) O (1, 5) O (4, 7) O f'(x) does not change sign at any of these points.

Q: 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of…

A: Derivative of a function is a slope of function on given point, or derivative is a rate of change of…

Q: Find the derivative of 3 -8 -5 -5 6 -5 1 0 -2 8 -6 -9 1 -3 0 0 0 -2 0 | f(x) = det -1 0 6 -4 ОА. -…

A:

Q: Q-2) Prove that converting the Higher-Order derivatives to the finite difference formula would be:…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Use the Chain Rule to express the second derivative off o gin terms of the first and second…

A: Let y=f o g then we have to find the second derivative of y.

Q: Suppose the function V represents the number of people vaccinated for COVID-19 in Kalamazoo country.…

A: Given : V represents the number of people vaccinated for COVID-19 in Kalamazoo country. To…

Q: What is the derivative of f(x) = %3D (² - (z – 1)")* 02 (2 – (a – 1)°) (-3z² + 8z – 3) O2 (2² - (2 –…

A:

Q: Find the hundredth derivative of the function f (x) = cos(2x). O f(100) (x) = -2!00 cos(2x) O f(100)…

A:

Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: 13. Find the derivative of y = in terms of f, g, h, f', g' and h', where f, g, and h are functions…

A:

Q: Man, i have a simple question: Assuming that the derivative of f(x) is on the image, f(x) is…

A: Function f(x) is increasing in an interval if f'(x) > 0 in that interval. Hence, we need to find…

Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

A:

Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

A:

Q: Question 1. A critical point of the function g(x, y) = ex y + 3x²y-y is (0,0). Use the Second…

A: Explained below

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: sinx 2x-x-1…

A:

Q: ion ƒ(x) is infinitely differentiable and that f'(x) = - st, second, third and n-th derivative of f…

A:

Q: Compute all second derivatives of f(1.y) = (x+) e- %3D

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: 47. Determine the first and second derivatives of the function f(x) tan" (x² – x +1) tan %3D at x=1…

A: Given: The function, fx=tan-1x2-x+1   To determine: The first and second derivatives of the given…

Q: Gottfried Leibniz, one of the inventors of calculus, initially thought that the derivative of…

A:

Q: If f(x) is odd function, then the derivative of y =sinh (-x)) equals Select one: f'(x) O y'=- V…

A:

Q: Gottfried​ Leibniz, one of the inventors of​ calculus, initially thought that the derivative of​…

A:

Q: If f(x) is odd function, then the derivative of y=sinh (f (-x)) equals Select one: o y'=Xf'x) – f x)…

A: Differentiate wrt x

Q: OFind the derivative of the 1 +5 (a). f(z) = %3D T2-5

A: As per the guidelines we can solve only one question at a time so if you need more answers then…

Q: 2. Find the derivative of f(x). (a) f(x) = x² sec x (b) f(x) = 1+ tan a 1- tanz

A:

Q: Why does the maximum and minimum points for y = f (x) occur among the minimum and maximum points for…

A:

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: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: 3. Find the derivative of f(x). (a) f(x) = e cos x (b) f(x) = (2x³ 4x-¹) cotx -

A:

Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

A:

Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

A: f(x) = xk and we need to find all the derivatives of f(x)

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: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: Compute the derivative of g(x) = cos(t²) dt. O 42 sin(z*) O cos(x*) -42 sin(z*) O 4a cos(a) O -…

A:

Q: The derivative of the function y = x(tan-'(3x))² is: y' tan (3x) 6x + (1+9x²) tan-³(3x)] tan…

A: y = x(tan-(3x))2 dy/dx = (dx/dx)(tan-(3x))2 + x(2(tan-(3x))(3))/((3x)2 +1) dy/dx = tan-(3x))2 +…

Q: 24. Estimate instantaneous rate of change of each function at the given x value using a centered…

A: Given :-  The instantaneous rate of change of each function at the given x value using a centred…

Q: How do I find the 20th derivative of f(x)=(2cos x)(cos 3x)? I think there must be some trick because…

A: Given:

Q: 5* The derivative of the function: f(x)= 5* + 7 7.5 In5 (5* – 7)2 7(5 In5) (5 + 7) 7(5*ln5) (5* +…

A: According to the problem, we have

Q: ind the 9th derivative of f(z)=exp((-1 + isqrt 3)z) at z=0.

A: Given f(z)=e(-1+3)z Differentiating w.r.t 'z' f'(z)=e(-1+3)z(-1+i3) f''(z)=e(-1+3)z(-1+i3)2…

Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

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: (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: 2) Use the Chain Rule to express the second derivative of ƒ • g in terms of the first and second…

A:

Q: Find the first derivative of g(x) = 2 In(x)tan(x*). g'(æ) = %3D

A: Given that g(x) = 2ln(x) tan(x^4). Find first derivative of this function. We know that derivative…

Q: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

A:

Q: True or false: if f is continuous at a, then the derivative of f exists at a. If it is false, can…

A: To find  -- if f is continuous at a, then the derivative of f exists at a or not.

Q: 10.Anti-derivative of y(2y^2-3)^5

A:

Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The…

A: f(x)=ln…

Q: Let f(x) =x. cos(x2). What is the correct result of the derivative of f with respect to x? =X•COS…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.