Supppse f(x) =. Estimate f'(2), f'(3), and f'(4). What do you notice? Guess a formula for f'(x). NOTE: Roud your answers to the nearest integer. f'(2) = f'(3) =| f'(4) = %3D f'(x) =

Q: the estimate of solution to x=2^-x to 4 decimal places is what?

A:

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: Find the derivative of the function. 1 In(1 + 49x 14 y = x arctan 7x dy

A: Given y = xtan-1(7x) -114ln(1+49x2)dydx = d xtan-1(7x) -114ln(1+49x2)dxdydx =…

Q: Find dy/dx by implicit differentiation.

A: To find: The derivative of x3y-xy3=4. Concept used: Chain rule of derivative: fgx'=f'gx·fgx Product…

Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

A:

Q: Find the derivative of the function. y = 3x e -X - 3 ex3 dy dx

A:

Q: find nth derivative of y=x/(x+1)^4

A: To find the nth derivative of the function y=x(x+1)4=x+1-1(x+1)4=1(x+1)3-1(x+1)4

Q: 5. y= 2arctan(vx)

A: We need to evaluate the derivative of the following function y = 2arctanx

Q: Find the general solution using reduction of order. 1. y''=ln(x)

A:

Q: Use the first derivative test to find the location of all local extrema in the interval for the…

A:

Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

Q: SW Solve for the first derivative of ,(x+5) x' +e x³ +e + Vx f (x) = V0.1 at x= 0.05 using FCD BCD…

A: f'(0.05)=336.6222-333.90350.008=2.71870.008=339.8375 App value of f'=339.8375 exact value of…

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

A:

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cose

A: The given function is : s(θ)=200sinθcosθ We need to find the derivative in two ways.

Q: 10. S(2x – 3) dx e 2x2 - ебх

A:

Q: 2) Find nth derivative of the following function f(x) = ex

A: Given query is to find the nth derivative of the expression.

Q: Use forward and backward difference formula with h = 0.1 to approximate the derivative of f(x) =…

A:

Q: Find the derivative of the function y = (1/2) arctan e2x

A: Given function is y=12tan-1e2x Chain rule of differentiation states that: ddxfgx=f'gxg'x And also we…

Q: Find the derivative of the function. h(x) = x² arctan(5x) h'(x) =

A: h(x)=x2tan-1(x)

Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

A:

Q: Find the derivative of the function g(x)= integral  x2  tanx  (1/square root 4+t4) dt

A: Leibnitz integral rule for Differentiation :               ddx ∫α(x)β(x) f(t,x) dt = ∫α(x)β(x)…

Q: Use implicit differentiation and solve for dy/dx if 6x+(x^3)y+3y^2=10.

A: The technique of implicit differentiation allows us to find the derivative of y with respect to x…

Q: Find where the first derivative is equal to 0. Er ****. lif

A: Introduction: The concept of critical point is very important in Calculus as it is used widely in…

Q: Estimate x² dx using left endpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: The equation of the integral function is ∫03x2dx. The left endpoints is n=4.

Q: The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent per…

A: Given,    no. of tent = 25 ,  average no. of cases=6

Q: Find the derivative of the function tanh-e* A. -1/2 csch x B. 1/2 csch x C. -1/2 csch 2x D. -1/2…

A:

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

A:

Q: What is the first derivative of s(æ) = 4e"*.

A:

Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

A: Note:- For this problem, you don't mention any particular method and anything about h. So, I'll try…

Q: 7. Find the nth derivative of y = 1//x.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: what is the derivative of f(x)=ln(tanhx)

A:

Q: Find the second derivative if y = sinh- (n + x') at x = 0

A:

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: Q2: What is the value of second derivative of f(x)=3 sin((1-x)/t) *

A:

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

A:

Q: 2. If f (x) = xV x + 3, find the derivative of this function and the slope of the tangent line at…

A: Product rule of differentiation: (fg)'=fg'+gf' The slope of a tangent line at (a,b) is given by:…

Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.5x² –…

A:

Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

A:

Q: The derivative of y=eSinh/x +cosh¬/x equals

A:

Q: The derivative of x at X = 1 is to I Frue or false 2

A:

Q: Find the nth derivative of the function y=xlnx at x=1.

A:

Q: Find the derivative of the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

A:

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: Find the derivative of the function y, below. y = 2x(ln x + In 7) – 2x + V2 dy da

A:

Q: Find the derivative. f(x)=tanh(2 + e^3x)

A:

Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

A:

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

A: