Find the approximate value of second derivative f"(0) with the step h for the following function by using midpoint formula: f(x)=x³ – x, h= -16 16 32 4

Q: Find the derivative of the function y=(ex−1)(ex+2) and calculate its value at x=0.

A: Differentiating with respect to x, we get

Q: Find y'(x) from y(z) using the definition of a derivative.

A: according to the problem, we have

Q: Find the second derivative for the functions defined as follows.h(x) = x/ex

A: Given:             f(x)=xex

Q: Find the derivative of the functionf(x) = Vx – 2. Provide your answer below: f'(x) =O

A: We have to find derivative

Q: Use the second derivative test to find the extreme values of the function J () = x³ – su² 24X .

A:

Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

A:

Q: Given the function y=x2cos3x. Find the third-order derivative.

A: To Determine: Third derivative of given function:

Q: 2. Calculate the derivative by first principles for the following: i. f(x)=Vx,

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: Use three-point midpoint formula to evaluate the first derivative of y = x² + 4x − 5 at x = 0 using…

A: The given problem is to find the first derivative of the given function at x=0 with given h value by…

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A:

Q: Find the derivative of the irrational function y=m√xn where m≠0

A: we have to find the derivative of the irrational function y=mxn

Q: 2. Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1,1) in the direction…

A:

Q: Find the given higher-order derivative. F(3)(x) = Vx², f(4)(x) f(4)(x) =

A: Given that, the higher order derivative f(3)(x) = x23 To find the higher order derivative of f(4)(x)…

Q: 2. For y = 6x*V4 + x, find y(2).

A:

Q: Q2. Use the definition of the derivative to find ý of the function y = sin(x). %3D

A: Here given function is  y = sin(x)

Q: Of the two functions f and g in Figure , which is the derivative of the other? Justify your answer.

A: Given Graph,

Q: Find the nth-order derivative of the function y=(3x2−2x)lnx, x>0.

A: Use the product rule

Q: 2. y = 1 (tanh~' 2x)3

A:

Q: Find the derivative of the function y=ex+2ex at x=0.

A: Given: y=ex+2ex=3ex we know that ddxkex=kex

Q: Evaluate the derivative at x = 1 for y = I (

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Q /Choose the appropriate derivative for this function y = (x + 1)²¯*

A: Given equation:y = (x+1)2-x required:1) dydxSol:y = (x+1)2-x →taking logarithms on both sides we…

Q: Q2: - Find the second derivative of the following function at x = 2 15 marks 1) y=+ V 2) y 3 (x +)…

A:

Q: Find the derivative of the function. S(2) = VE - 8E f (x) =

A: topic - derivative of a function

Q: Determine the 3rd derivative of the function y=x3/x+2 at x=−1.

A:

Q: find the most general anti derivative  f(x) = e^2

A: A function F(x) is called an antiderivative of f(x) if F’(x) = f(x).   The function f(x) is the…

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: B. By using the definition of the derivative, find the for: dx 1- f(x) = V %3D 2- f(x) = x -!

A:

Q: Q1. By using the “definition of the derivative" find of y = v2x? %3D dx

A: Explanation and solutions is given below....

Q: Find the derivative of the following using the three-step rule Зх — 1 1. y= 2х+5 2. y=Va? +x?

A:

Q: Find the derivative of the following using the three-step rule Зх-1 1. у3 2x +5 2. y=Va² +x?

A: Using three step rule.

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: Find the derivative of the function using the Power Rule for Functions. y = (x² + 6)²(4x³ – 1)3 dy…

A: Y'= ?

Q: Find the first derivative of the function * 4 f (x) = Væ + 4

A:

Q: Solve for the derivative of y IMPLICITLY 22 + Væ3 + 2y= y²

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the second derivative f"(x) for f(r) = e(z+2)*.

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

Q: find the derivative using the definition ƒ(t) = 1/2t + 1

A: Given:ft=12t+1Derivative definition:f'x=limh→0fx+h-fxh

Q: Use the Chain rule with other differentiation rules to find the derivative of the following…

A:

Q: Find the derivative of the function. f(x) = e In( Vx + 8 f'(x) =

A: Given, f(x) = ex ln(x+8) We have the formulas d(ex)/dx = ex                       ...........(1)…

Q: Find the derivative of the function f(x) = V (x² – 2)* at x = 1.

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: Find the nth order derivative of the power function y=xm where m is a real number.

A:

Q: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition

Q: Solve by definition of derivative if f(x)=x+Vx AND also Find x? w.r.t x*

A: fx=x+x Now by the definition of derivative, we have…

Q: The derivative of the function y = 2* sec(x²) is:

A: I use product rule and chain rule to solve this derivative

Q: Q2: - Find the second derivative of the following function at x = 2 1) y=+ V

A: ddx1x = -1x2 ddxxn = nxn-1 ddxx =12x

Q: Find the approximate value of derivative f(0) with the step size h for the following function by…

A:

Q: Find the higher order derivatives for f (x)=x^5, what is f^(6) (x)?

A: According to the given information f(x) = x5 and it is needed to calculate f6(x).Since, if p(x) is a…

Q: Find the derivative, or y', of ³ – Vy = ¿y² + 6 at (2,1).

A:

Q: Use forward-difference formula to evaluate the first derivative of y = x² + 4x – 5 at a = 0 using a…

A: The forward difference formula is : f'(x)=f(x+h)-f(x)hWe have to find the first derivative of…

Q: Q2: A) Find an equation of the line tangent to the function of x² + (y-x)2 9 at x 1. dy x-x3 B)…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: