84. Use the definition of the derivative to directly prove thedifferentiation rules for constant and identity functions

Q: Use the definition of the derivative to find the slope of the tangent line to the graph of the…

A:

Q: 2. how does the knowledge of differentiability and continuity determine the derivative of functions?

A: A function is said to be differentiable if the derivative of a function exists at all points. The…

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

A: Given,

Q: f(x) = (x + 2)2/3 -

A: First we have to find f'(x) . And to find extrema by first derivative test we have to find all roots…

Q: use the limit definition of a derivative to find f'(x) f(x)= sqrtx+5

A: See the details solution in below

Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

A:

Q: Find f' usip , derivative rues Fの =x°(x -ス) %3D

A:

Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: use the definition of derivative to find the equation of the tangent line to the graph of f(x) = x2…

A: To find the equation of tangent line at the given point.

Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

A:

Q: Prove, using the definition of derivative, that if f(x)  = Cps x,then f'(x) =- Sin x

A: Given fx=cos xBy definition of derivativef'x=limh→0 fx+h-fxhfx=cos xThereforef'x=limh→0 cosx+h-cos…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A: Given function is : fx=6x2 To find out slope of tangent at x=2 , Differentiate fx with respect to x,…

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

A:

Q: Use the limit definition of derivative to compute the derivative of ​f(x)equals=44xcubed3. Find…

A: From the given information:

Q: Suppose that the function y in the Derivative Product Rule has a constant value c. What does the…

A: Derivative product rule:The derivative product rule for the functions x and y is given by,

Q: 1 . Use the definition of the derivative to compute f'(x) if f(x)

A: We use the limit definition of f'(x)

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: Use definition to find the derivative of the function f (x) = 5x- 2x at = 3. [2 Marks] %3D

A:

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: et + 6x Compute the derivative of -3 -2x (simplification not necessary)

A:

Q: 16. Use the limit definition of the derivative to find the instantaneous rate of change for the…

A:

Q: Use the formal definition to find the derivative of f(x) = 4 at x = 8. x+3

A: To find the derivative of the function  f(x)=4x+3 at x=8

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: 12, for f(x) n(x) Estimate the slope of the tangent line at the point x (Use decimal notation. Give…

A: Given,

Q: se the General Power Rule to find the derivative of the f y = 124x2 + 5

A:

Q: Use the linut definition to Compute f(x) when f)-at. the derivative f(x) when f)-2+L

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: show that the function is derivable and that the derivative is continuous.

A: The objective is to show that the given function is derivable and the derivative is continuous.…

Q: 23: USE THE DEFINITION OF THE DERIVATIVE to find the derivative: :9(x)=3

A:

Q: Let f(x)=9−(4x^2+3x). Then according to the definition of derivative

A:

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

A:

Q: 5, Find derivative y = Cott-tanx

A: We will find the derivative as following.

Q: Use the definition of derivative to find the slope of the tangent line to the function f(x) = V2x at…

A: Let's find.

Q: f'(x) at x if f(x) = csc³(x).

A:

Q: = Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x)…

A:

Q: 2) Usc the product rule to find the derivative of y= (4x+5) (x² 2x)

A: The given expression is : y=4x+5(x3-2x)             …(1) If y=uv Applying product rule on above…

Q: What is the limit that will calculate the derivative f'(2) for the function f(x)= x-1

A: solution of the given problem is below...

Q: Give three different notations for the derivative of ƒ with respectto x

A: Definition used -     Derivative of a function -       It is the rate at which the y value of…

Q: 9. Use the definition of a derivative change of the functions below at f(x)% = x² + 2x

A:

Q: 10 Use the power rule to find the derivative of f(x) = Vx.

A: Given,          The function is fx=x10 .

Q: What is the slope of the tangent line at (0,3) to the function f(x) = -sinx+3

A:

Q: 2. Use the definition of the derivative to find f'(7) if f(x) = 4 + 3x – 2x.

A:

Q: 13 Use the power rule to find the derivative of f(x) = 'Vx.

A:

Q: 11. Find the derivative of tan x by using the quotient rule.

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

A:

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) 7x² + 2x…

A:

Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…

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: