1. Let f(x) = mx + b, the line with slope m and y-intercept b. Use the rules of differentiation to show that f'(x) = m. This again proves that the derivative of a line is just the slope of the line.

Q: With respect to x, what is the derivative of: * du In(u) O Option 2 Option 4 du Option1 Option3

A: apply chain rule

Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

Q: A function is given as x - 6y = 5– x. Calculate the derivative of y with respect to r with two…

A:

Q: 1. If y = x³ + x - 5 then what is the derivative of y with respect to x?

A: Derivative of a function

Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

A:

Q: 1. Use the definition of the derivative to find the derivative of the following functions. 1 (b)…

A: use definition of derivative to find the derivative of the following functions a) fx=x+2 it is known…

Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

Q: Suppose that f'(0) = 2. Find the derivative of the function (e2z – 2x)f(3x) at x = 0.

A: Given that f'(0)=2.Our Aim is to find the derivative of the function (e2x-2x)f(3x)-(i) at x=0.

Q: In what directions is the derivative of ƒ(x, y) = (x2 - y2 )/ (x2 + y2 ) at P(1, 1) equal to zero?

A: Given, , the unit vector is , here directional derivative is given as,

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

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: 2. Calculate the derivative of the following. y = (x*- 3x2+5x) 3 y = tan (x2 + 5x - 2) А. B. (4x +…

A: Given  A. y=(x4-3x2+5x)3 B. y=tan2(x2+5x-2)C. y=(4x+3)3(x-2)2D. y=x2ex2-1

Q: Find the derivative of y with respect to X, t, or 0, as appropriate. Inx y=5

A: Given: y=ln xx5 So, the derivative of y with respect to x is: dydx=ddxln xx5 According to the…

Q: Suppose In (x + 2y) = x*. Use implicit differentiation to find the derivative of y with respect to…

A:

Q: or x>0, determine the deriva

A: Consider the given function: Here the objective is to find the derivative of a given function using…

Q: A) Find an equation of the line tangent to the function of x2 + (y – x)² = 9 at x = 1. dy 3) Using…

A: A).Givenx2+(y-x)2=9(y-x)2=9-x2y-x=±9-x2y=±9-x2+x -----{1}Taking positive of equation {1}y=9-x2+xNow…

Q: Find the derivative of the function y=2x+12x−1 at x=1.

A:

Q: Obtain the derivative of the function y (3 sen(4x))° ( tgʻ(2x)) y = (sec(2x))* – 1

A: This question is based on Trignometric application and diffrentiation of function.

Q: Let ƒ(x) = √2x + 1. Compute ƒ'(2),the derivative of ƒ at x = 2, and use the result to find an…

A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

Q: Why is the derivative of f(x) = e^2, 0? Would e to any power be 0?

A: Given f(x)=e2As the given function is in terms of x and the given function e2 is a constant

Q: Find the derivative of the function.

A: Some important derivative formulas: 1. d(lnx)/dx = 1/x 2. d(√x)/dx = 1/(2√x) 3. d[N/D]/dx = [D*(N)'…

Q: 15 - What is the approximate derivative of f(x) = 5x° + 4x? if we use forward difference method,…

A: Derivative of function at any point gives the slope of tangent to the function at that point.…

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

A:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: Give two different interpretations of the derivative of the function y = f(x) at x = a.

A: If f(x) represents a quantity at any x then the derivative f′(a) represents the instantaneous rate…

Q: Find the derivative of y with respect to the appropriate variable. y= cosh 2x+2 O A. V(4x + 9)(x +…

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Q: _6. What is the derivative of f(x) = (5 – x²)²? а. 2(5- х2) b. 10 – 2x2 C. 4x3 – 20x d.(5 - x?)(5 -…

A:

Q: Let y=x(lnx)^2. Find the value of x for which the second derivative y"(x), equals zero.

A:

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 derivative of the function y=(x−1)(x−2)(x−3) at x=0.

A:

Q: Calculate the derivative of the function y(x) given by the equation x2+2xy+2y2=1 under condition…

A: For y=1 we find x

Q: Suppose In (x + 2y) = xª. Use implicit differentiation to find the derivative of y with respect to…

A:

Q: Find the 10th-order derivative of the function y=(x2+4x+1)√ex at the point x=0.

A:

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A:

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 derivative of y with respect to x, t, or 0, as appropriate. In x 20) у 3

A: Given

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: Suppose In (x + 2y) = x4. %3D Use implicit differentiation to find the derivative of y with respect…

A: Given, lnx+2y=x4                  ....(1)

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

A:

Q: Find the derivative of y with respect to t. y = 5sin (4t)

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 ofy. with respect to x if y=(Ix +5) (9x² +2x) %3D

A: Given that: y=(x+5)(9x2+2x)

Q: Find the derivative of y with respect to x if y = (10x- 20x + 20) ex. %3D dy dx

A: We can make it easier for you

Q: Use backward, forward , and centered difference approximation to estimate the second derivative of…

A: The formulas for the backward, forward, and central differences to approximate the second derivative…

Q: If g(z) = 6z-2), then its derivative is given by:

A: For simplification, take natural logarithm on both sides of the equation gx=6x2-2 and apply the…

Q: Suppose ln (x + 2y) = x4.Use implicit differentiation to find the derivative of y with respect to x.…

A: Differentiate the given function implicitly as follows.

Q: Find the derivative of y with respect to x. 3. (x² + y²)² =ay²

A: The equation given to us is

Q: Find the derivative of the function. (x-7)(x²+2x) +3 y = O A. OB. dy dx O D. dy dx dy O C. dx dy dx…

A: