89. Use the definition of the derivative to prove the quotientrule. (Hint: At some point you will have to add and subtractthe quantity f(x)g(x) from the numerator.)

Q: Use the limit definition of the derivative to find f'(x). f(x)= 2/x+3

A:

Q: Use the limit definition to calculate the derivative of the linear function. f (x) = 7x − 9

A: Plug the given function in the limit definition of the derivative

Q: Show that the derivative of FOx) =x² is f'x)=2x using the defimition

A:

Q: Use the formal definition of the derivative to find f'(x) is f(x)=x²-4x

A: See the details solution in below

Q: Use one of the limit definitions to find the derivative of f(x) at x = 2. f(x) = 4x2

A: Explained below

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=3f(x)+1x. If the…

A: Derivative of a function using the formula f′(x)=3f(x)+1x and f(3)=6. We know that approximate…

Q: use the limit definition of deruvative to find the derivative of the given function. f(x)=5x2-3x+10

A: Given function f(x) = 5x2-3x+10using the limit definition of derivative , we have to find the…

Q: Find the derivative of the function f(x) = In(2a? + 5æ)

A: ddxln (x)=1xddxxn= n xn-1

Q: se the definition of a derivative to find f '(x) and f"(x). f(x) = 3x² + 6x + 3

A: Given,           fx=3x2+6x+3

Q: Use the limit definition of the derivative to find f'(x). f (x) = Vx + 5.

A:

Q: f(x) = In (3x + e3x)

A:

Q: Find the derivative with respect to x of f(x) = 2(x + 5)* + 3(x + 5)° + (x + 5)² + 4.

A: The given function, f(x)=2x+54+3x+53+x+52+4

Q: Suppose the derivative of a function f is f'(x) = (x + 2)ª(x – 3)³(x – 4)6. on what interval is f…

A: f'(x) > 0  For increasing.

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

A: From the given information:

Q: Use the limit definition of the derivative to find f'(x) given that  f(x)=1/(x+5)

A: The given function is f(x)=1x+5 Use the limit definition to find derivative…

Q: If f(x) = 24x + 2, use the limit definition of the derivative to find the instantaneous rate of…

A:

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: Suppose f (x) =In( 2x³– 5x). What is the derivative of f with respect to x?

A:

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: What rule should be used in getting the derivative of a.)  f(x) = x^5 b.) h(x) = 3(x + 4)^3 c.)…

A: a. fx=x5 The rule used to get the derivative of given function is, ddxxn=nxn-1 The derivative is,…

Q: Use the limit definition of the derivative to find f'(x) given that 1 f (x) = x + 5°

A: Given: fx=1x+5 we know that f'x is given by f'x=limh→0fx+h-fxx+h-x

Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

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

A:

Q: Q8.) By using the definition of the derivative, find the equation of the tangent line to the graph…

A: Please see the answer in Step 2

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: Use the limit definition of a derivative to solve the following of f'(x) f(x)=4x2-x+1

A:

Q: 84. Use the definition of the derivative to directly prove thedifferentiation rules for constant and…

A: The definition of derivative states that: f'x=limh→0fx+h-fxh Let the function be fx=c, where c is a…

Q: Calculate the following derivative if h(w) = √webw (Use symbolic notation and fractions where…

A: see below the answer and calculation

Q: f'(x) = (x + 2)*(x – 4)7(x – 5)6.

A: Given that f'x=x+24x-47x-56To find : on what interval f is increasingsolution :if f'x is positive…

Q: Use the definition of derivative to find = f'(x). f(x) = for 1 3x

A: Given f(x)=13xf'(x)=limh→0f(x+h)-f(x)h=limh→0(13(x+h))-13xh=limh→013x+3h-13xh

Q: Calculate the following derivative if f(x) = 5e* - x³. %3D (Use symbolic notation and fractions…

A:

Q: 1) Use the definition of the derivative to calculate the derivative off(x) = 3x2-5x+ 1

A: Find the derivative of f (x) = 3x2 –5x +1.

Q: Use the limit definition of the derivative to find f'(x). 2x f(x) = x+3

A: Given function is

Q: use the limit definition of deruvative to find the derivative of the given function. f(x)=-5x+79

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: use the limit definition of a derivative to find f'(x) f(x)=1/x+3

A:

Q: The derivative and antiderivative of a function are unique. O True False

A: derivative of a function is always unique  but integration is not unique, it depends on constant…

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

A:

Q: The order of diff. eq. is the high * .derivative that acquire in DE True False O

A: The statement is given by '' The order of differential equation is the high derivative that acquire…

Q: Suppose the derivative of a function fis f'(x) =(x + 1)°(x÷ 3) xH6) On what interval is finereasing?…

A: For f to be increasing, f' must be positive.

Q: If f(x) : ,then what is the derivative of f(x) with respect to x? O 10 x3 10 10 -- x3 O 10 x2

A:

Q: Suppose the derivative of a function f is f '(x) = (x + 1)2(x − 2)7(x − 3)4. On what interval is f…

A:

Q: Suppose the derivative of a function f is f'(x) = (x + 2)(x - 5)5(x - 6)8. On what interval is…

A:

Q: Suppose that f(x) = 5x - 2x. Use the limit definition of the derivative to find: (a) The slope of…

A: Given: y=f(x)=5x2-2x To find: the slope of the tangent line, the instantaneous rate of change and…

Q: Use the Limit definition of the derivative to find the following derivative f (x)=  1…

A:

Q: Find the derivative of the function y = 3x? – 4x + 7 using limit definition.

A: Given: y=3x2-4x+7

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: