Use the definition of the derivative to find the derivative of the function f (x) = 1 Then find all x-values (if any) where the tangent line is horizontal. If the tangent 2/3x line is horizontal for all x, write R for your answer. If the tangent line is never horizontal, write None for your answer.

Q: Use the Quotient Rule to find the derivative of the function. f(x) = x/x-2   f '(x) =

A: Given function

Q: Use the definition of the derivative to differentiate the following function.    f(x) =1/2x^2+ 5.…

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Q: Use the derivative to find for which values of c the function 1 f(x) = CI+ x2 +3

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Q: Use the definition of the derivative to find the derivative of the following functions. 1. f(x) = 6

A: The derivative of a function y=f(x) is given by f'x=limh→0fx+h-fxh. The given function is fx=6.

Q: Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x) =…

A: Given f(x) = 3x then f'(x) = limh→0f(x+h)-f(x)h= limh→03x+h-3xh= limh→03x-3x-3hx(x+h)h=…

Q: Given the derivative of the function, use sign chart to determine the interval(s) on which f is…

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Q: Use the power rule to find the derivative of f(x) = x – 14

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Q: Find the derivative of the function by using the Quotient Rule. Simplify your answer. x2. - 4x + 3…

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Q: Use the Product Rule to find the derivative of the function.

A: Given :           The function h(x) = xx3 + 1 To find the derivative of h(x) using product rule.

Q: Use the Quotient Rule to find the derivative of the function.                           h(x) =…

A:

Q: Use the rules of differentiation to find the derivative of the function.

A: Given :              The function is f(x) = x + 11 To find :              The derivative of the…

Q: Use the definition of the derivative to find the value of f'(2) if f(x)=x'-2x. Then use it to write…

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Q: Find the second derivative for the functions defined as follows ƒ(x) = (x2 - 1)2

A: Given function: fx=x2-12 fx=x4-2x2+1 Differentiate the equation w.r.t "x"…

Q: Use the definition of the derivative to find the derivative of the function h(x) = x+3 then find the…

A:

Q: Use formulas (1) and (2) and the power rule to find the derivatives of f (x) = 1/x3

A: Definition used -                     1am=a-m            Power rule of derivative -…

Q: If f(x) = use the definition of the derivative to find f.

A:

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

A: Given that f(x)=x2-9 , c=8 find the derivative at x=c by using alternate form of derivative

Q: Use the definition of the derivative to find the derivative of the function f(x) then find the slope…

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Q: Use the alternate form of the derivative to find the derivative at x-c, if it exists. f(x) = x³ +2x2…

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Q: Use the Quotient Rule to find the derivative of the function. h(x) =  x2 x + 7 h'(x) =

A: Consider the provided function:

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

A: Given data:   The expression for the given is h(x)=|x+5|. The given point is c=-5.   The expression…

Q: Use the definition of the derivative to determine the derivative of the following function:  f(x)…

A: Solution by definition of derivative :-

Q: By definition, find the derivative: f (x)= Vx

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Q: Use the definition of the derivative to find the derivative of the function f (x) 18. Answer f'(x) =…

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Q: Use the rules of differentiation to find the derivative of the function.

A: Given,

Q: Given the derivative f'(x), find the x-value for all relative extreme for the graph of the original…

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Q: Differentiate the following functions, using the definition of derivative. f(x) = x2 + 2 a.

A: For a small change h in x solve the limit for derivative of f(x) .

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

A: Proceed as shown below

Q: Find the derivative of the function f(x) = 34x

A: The given function is fx=34x.

Q: Use the rules of differentiation to find the derivative of the function. y = x12

A: The given function is y=x12 rule used: ddxxn=nxn-1

Q: Use the definition of the derivative to find the derivative of each function with respect to x. 1)…

A: Given: The functions in x is given.         1) fx=-4x-22) y=4x2+13) fx=-3x2+4 Objective is to find…

Q: Use the General Power Rule where appropriate to find the derivative of the following functions.

A:

Q: find the derivative of the function: sqrt(x/(x+1))

A: topic - derivative of a function

Q: Find the derivative of the function   in two ways: by using the Quotient Rule and by…

A: x4−5x3+xx2 Given function f(x)=ddx[x4−5x3+xx2] Recall Quotient Rule  ddxxy=ydxdx-xdydxy2

Q: Use the Quotient Rule to find the derivative of the function.                                f(x) =…

A:

Q: Use the Quotient Rule to find the derivative of the function. 2х — 3 g(x) x - 1 g'(x) = %3D

A: Given that gx=2x-3x2-1

Q: Let ƒ(x) = x2, Find the derivative

A: ddxxn=n xn-1

Q: Use the Quotient Rule to find the derivative of the function. x2 h(x) %D x + 4 h'(x) =

A:

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (х) - х2…

A:

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: 4. x – 2x² +x-1 g(x)=x

A: topic -derivative note : as per bartleby guidelines, we are supposed to answer only first question…

Q: Find the derivative of the following function by applying the appropriate derivative rules. f(x) =…

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Q: Find the derivative of f(x) = x3 + 2x, use the definition of the derivative

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Q: f(x)=

A: we know derivative rules, Common Functions Function Derivative Difference Rule f - g f' − g'…

Q: Use the definition of the derivative to find the derivative of the function g(x) = 4 –x², then find…

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Q: .If f(2) = 3 and f'(2) = 5, find an equation of the tangent line at the point where x=2.

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Q: Use the definition of a derivative to find f'(x) for f(x) = v2x

A: Solution:Given     f(x)=2xTo find f'(x)Formula:By the defition of derivativef'(x)=limh→0f(x+h)-f(x)h

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

A: Here we use the alternative form of the derivative to find the derivative at x=c Where…

Q: Use the rules of differentiation to find the derivative of the function. f(x) = −9

A: Given, f(x) = −9   To evaluate f'(x)=?

Q: 4 b) g(x)=15x* In x

A: Given that, the function is gx=15x4 lnx.

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: