The notation f(x) describes the value of at

Q: Let f(x)=x2 - 3 Use the definition of the derivative to find f1 and f11 Write answer in form of…

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Q: Find the derivative of the function using the power rule. (a) f(x) = 3/5x5 − 4x −4/3x-3 (b) f(x) =…

A: a) f(x)=35x5-4x-43x-3 f'(x)=ddx35x5-4x-43x-3       =35ddx1x5-4ddxx-43ddx1x-3…

Q: Find the function f(x) such that f'(x) = f(x)(1 – f(x)) and f(0) = . (Use f for f(x) in your…

A: Solution:

Q: 2х-9 F(x)% = %3D 4х

A: We have to find the definition of the derivative to find f(x). By the definition of the derivative,…

Q: Find the first derivative f' and the original function ƒ. f"(x) = x³ - 16x + 4, f'(0) = 3, ƒ(0) = 2…

A: Solve the following

Q: Differentiate f(x) = a4x4 -3ax² with respect to x. Assume that a is a constant. f'(x) =

A: f(x)=ax4-3ax2 differentiate with respect to x

Q: Use the Product Rule to calculate the derivative. f(x) = (7x + 2) (4x² – 3) (Use symbolic notation…

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Q: Calculate the derivative. f(x) = (6ex - 7x²) (x³ + 1) (Use symbolic notation and fractions where…

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Q: find the derivative  f(x)=x3(x2-1/x2+1)

A: Given:The function f(x) = x3 (x2 − 1)/ (x2 + 1)

Q: Find the indicated derivative using the definition f(x) = 2x4+3x3-2x+7: f'(0)

A: Differentiation is the rate of change in the value of the dependent variable with respect to the…

Q: The function f is given by f (x) = (1+x)=. How do the values of f behave for small positive and…

A: Here we define  f  for small or large positive value of x.

Q: Use the product rule to calculate the derivative  f(x)=x^3(2x^2+1)

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Q: 16) Find f'(x) using the definition of the derivative. f(x) = x3 + x

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Q: Use the Product Rule to calculate the derivative. f(x) = (2x - 9)(4ex + 1)

A: Definition used-                 Product rule of derivative -                     ddx(f(x)×g(x))=…

Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: he derivative to determine whether the function is strictly monotonic on its entire domain and…

Q: Differentiate  f and find the domain of f f(x)  =   x / ( 1 -  ln (x-1 ))

A: Given: fx=x1-lnx-1 we know that domain of given function is  1-lnx-1≠0lnx-1≠1…

Q: Use limits to compute the derivative.   f ′(4) if f(x)=3x3 f ′(4)=?

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Q: Find the indicated derivative.f '(x) for f(x) =(x + 3)(x − 4)x2 + 4

A: Given function f(x) = (x+3)(x-4)x2+4differentiating this function with respect to x we get…

Q: Use the Chain Rule to find the derivative. f(x) = (x5 – x3 – 1)2/5 %3D

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Q: Apply the definition of the derivative of a function to find f'(x). a. f(x) = 6x + 4 b. f(x) = x2 -…

A: To find the derivative of the function using the definition of the derivative. (a). Given function…

Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: f(x)=x3-6x2+12x

Q: 11. f(х) 3D 2x3 - 5х - 5x

A: Given- fx=2x3-5x To find- The derivative of the above function using defination of derivative.…

Q: Use the product rule to find the derivative. f(x) = (3x - 2)(6x + 1) %3D O f(x) = 36x - 4.5 !3! O…

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Q: f(2) — V3х — 7

A: Solved using terms of derivative.

Q: How to use the standard y = f(x) notation to indicate that (a, b) is an element of the function f?

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Q: Find the function f(x) such that f'(x) = f(x)(1 – f(x)) and f(0) = (Use f for f(x) in your…

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Q: Use the Product Rule to find the derivative of the function. g(x) = (x² – 6x + 7)(x³ – 1) g'(x) =

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Q: Let f(x) = 4x² +. Use the definition of the derivative to find f'(1). %3D

A: To find the derivative of f(x) at x=1 using the derivative definition.

Q: The derivative of is f (x) = 3x* + 7x² + 5x + 2 %3D

A: Given, f(x) = 3x4 +7x2 +5x +2

Q: Differentiate the function with respect to the independent variable. f(x) = 2x° In xº f'(x) =O

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Q: Find the derivative and simplify. f(x) = (x12 + 3x* + 5)(2x³ - 1) f'(x) = %3D

A: Some differentiation formulae: ddx(xn)=nxn-1ddx(c)=0  ; c is any consant value Given function is…

Q: Find the derivative of the algebraic function. f(x) = (x3 − x)(x2 + 2)(x2 + x − 1)

A: Given information: fx=x3-xx2+2x2+x-1

Q: 12. Find f'(x) using the definition of the derivative.  f(x) = x3+ x

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Q: f '(x) by using the definition of the derivative. f(x) = 4 – 6x2

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Q: Let f(x) = x-3 Use the definition of derivative to find f'(x). %3D 2C

A: Given : fx = xx-3

Q: Use the derivative f'(x) = (x - 3)(x + 4)(x + 4) to determine the maxima and minima of f and the…

A: f will be increasing if f'(x)>0. From the graph of f'(x) we see f'(x)>0 when x>3 [because…

Q: The derivative of the function has the same sign for all x in its domain, but the function is not…

A: Given, f(x) = x(x2 − 4) To prove f(x) is not one to one

Q: Use the Product Rule to calculate the derivative. f(x) = x³ (7x² + 1) %3D

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Q: Find the derivative. f (x) 7.) f(x)==x³+2x²–11 x–1 +2x²-11 x-1 6.

A: We have given

Q: Find the derivative. f(x) = 8/2x + 9 f'(x) =

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Q: find the derivative  f(x)=x2(x3-1)

A: Apply the product rule and obtain the derivative of the given function.

Q: Given use the definition of the derivative to show that f(x) = 4x + 3x- 1 f' (x) = 8x + 3

A: f(x)=4x2+3x-1 Definition of derivative:…

Q: Use the Product Rule to find the derivative of the function. g(x) = (x2 − 4x + 2)(x3 − 5)

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Q: find the derivative  f(x)= (x1/3-5)(x2/5-3x1/5+4x-1/3)

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Q: the derivative of f(x) = x% (x% +x% + x%

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Q: Calculate the derivative. f(x) = (4e* – 5x²) (x³ + 1) - (Use symbolic notation and fractions where…

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Q: Express the function in the form f◦g. f(x)=sec(x2)tan(x2).

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Q: Find an equation for f(x) using the secant function. f(x) = %3D

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