e) Use the definition of derivative to prove that your guess in part (d) is correct. 21-31 Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. Ons of etch the graph of f. nd f'(x). What are 27. g(x) = /9 28

Q: 1) Find the derivative of the given function with respects to e 3tan ở In 3 y

A: Given

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

A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: 1) Find the derivative of the given function with respects to e 3 tan 6 In 3 y

A:

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: 8. Suppose the derivative of the function y = f(x) is y' = (x – 1)*(x – 2)(x – 4). At what points,…

A:

Q: HiHtar is THe secoyd derivative OF Y

A:

Q: 4. Find the derivatives with respect to x of the function 2 – 3x^2. 5. Differentiate ax² + b to the…

A: Using derivative of composite function.

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: 8. Find the derivative of the following functions with respect to x by using either the product or…

A: Part (a):   Apply the product rule:

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: 4. The process of finding a general formula for the slope of a line tangent to a certain curve is…

A:

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: Suppose that the SECOND DERIVATIVE of a function f is given by f" (x) = (x – 2)² (x² – 4x). Find the…

A:

Q: 2 The derivative of (g(x))¯ is equal to (g '(x))¯. Select one: True False

A:

Q: 14. f(x) = 2 +3cos x

A: using basic properties and application of derivation we will solve this question.

Q: y = x*(1 – In x4)

A:

Q: Use the definition of a derivative to find f'(x) and f"(x), when f(x) = 2/x. I got f'(x) = -2/x2,…

A:

Q: 3. Calculate the derivative of the following functions. For this problem only, do not simplify your…

A: Given:          y=lnx2esin2x              =2lnxesin2x   differentiating on both sides…

Q: 2) NOT use the short cut method). Use the result to find the slope of the tangent line at the point…

A: Topic:- Derivative

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

A:

Q: 2. Sketch the graph of a tangent line of the function f(x) = at x = -1. And then find 1- x the…

A:

Q: 2. Determine the true error and relative true error when approximating the derivative of f (x) = -x²…

A:

Q: Find the derivative of the following function by definition (from first principle): f(x)= x/(x-1)

A:

Q: 1. Suppose that the revenue (in dollars) from the sale of x units of a certain product is given by…

A: The revenue function is given by Rx = 70x-0.05x2 To evaluate: The expression of R'(x) using the…

Q: (a) Let f(x)=√√2x+1. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

A:

Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

A:

Q: Suppose 8 (x) =sec='(x<). what is the derivative of g with respect to x?

A: We can find the answer as below.

Q: . Use Euler's method with a step of 0.1 to estimate f(2.5) if f(1)=-2 and the derivative of the…

A:

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

A:

Q: 1 6. Find the derivative of f(x)= 1 at the point 8, Vx+1

A: Given

Q: Compute the derivative of the function y = 6 cos- (7x) at the point x = (Use symbolic notation and…

A:

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

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: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

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

A:

Q: f(x) = x2 -1

A:

Q: 7. Consider the function f(x) X - 3 a. Using the definition of the derivative at a point, calculate…

A: Given : f(x) = x / x - 3   (1) f' (2)  (2) tangent line when x = 2 (3) normal line when x = 2

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

A: NOTE: Refresh your page if you can't see any equations. . the given equation is take x=-6

Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Let the function y(x) be given implicitly via the equation xy – In y = 2. Determine the value of its…

A:

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does…

A: Here the first derivative of the given function is y’= 6 x (x+1) (x-2). If a function has zero…

Q: 2. (a) Demonstrate the method of the limit definition of derivative to find the derivative of f(x) =…

A: Limit of differentiation

Q: 1. Use the definition of the derivative to find the derivative of f(x)- V-x-2

A:

Q: Find the derivative of the following function by definition (from first principle): f(x) = x-1

A:

Q: 1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 5л? + 3х — 14 (а) f(*) %3D 5х — 4 6x² + 4/x (b) f(x) = %3D

A:

Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

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: