Find the derivative of the function using the definition of derivative. f(x) px q f(x) State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.)

Q: f (x) = (x² – 1)**1

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Q: Q3\ Find the derivative of the following function by using the definition f(x) = x-1

A: Given function is fx=xx-1

Q: Find the derivative of the function at the given point (a) by approximating the definition of the…

A: Given: f(x)=x1x   To prove: Find the derivative of the function at the given point (a) by…

Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: The given function is fx=13x The definition of the derivative is shown below: f'x=limh→0fx+h-fxh

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: Find the derivative of the function.. 8 7 h(x) 218 4 х - h'(x)=

A: To find the drivative of the given function y=h(x)

Q: Use the General Power Rule to find the derivative of the function. g(x) = v6- 7x

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Q: Let g(x) = 7¯X. Find the derivative of the function g.

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Q: Find the derivative of the function g(x) et 5x - g'(x) =

A: We have to use quotient rule for derivative and use  d/dx(ex)=ex d/fx(ax+b)=a

Q: Q2/ Find the derivative of the function (x) =v3x-x by definition

A: Solve the limit for very small change in x .

Q: Find the derivative of the function below using the definition of the derivative. f(x) = 2³ + 2

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Q: Use the definition of the derivative to determine the derivatives of the following functions.   a.…

A: Part a,Given,         fx=1x3

Q: Find ƒ‴ (x) , the third derivative of ƒ, and ƒ (4) (x) , the fourth derivative of f, for function.

A: To Determine: The third and fourth derivative of fx=x2x+1

Q: Q3\ Find the derivative of the following function by using the definition f(x) = X-1

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Q: Find the derivative of the function. 1 g(x) x2 +o g'(x) =

A: Use the basic power rule of derivative and simplifie.

Q: Write the definition of the derivative of the function f(x) at the point x=x, Find using the…

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Q: Give the derivative formula for the function g(x) 2.1X 2 g '(x)

A: The given function is

Q: Find the derivative a) f(x) = (x2  - √x ) . ex b) g(x) = (x2)/ ( c + xex)

A: A) Find the derivative as shown below: f'x2-xex=ddxx2-xex                   =ddxx2-xex-ddxexx2-xex2…

Q: Given f(x) : , find f'(-1) using the definition of a derivative. x-2 Provide your answer below: f'(…

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

A: Solution by definition of derivative :-

Q: Find the derivative of the function f(x) = 8x2 – 13x by the definition of derivatives f(x + h) –…

A: on using this formula we get = 16x-13

Q: Give the derivative formula for the function. g(x) = 2.1* + g'(x) =

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Q: a) Using definition, compute the derivative function of f (x) = 4x7

A: Here, we will find derivative of given function by definition of derivative,

Q: Find the derivative of the function. x2 - 2x3 t(x) t'(x) =

A: In the question it is asked to calculate derivative of following function.

Q: Q1: Using the definition, calculate the derivative of the following function. f(x)=4-x

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Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

Q: Using the definition of derivative, find the derivative of the following functions: (a) y = xvx² -2…

A: (1) Y = X*(X2-2)0.5       dY/dX = (X2-2)0.5  + (1/2) *(1/(X2-2)0.5) *…

Q: Consider the function: y = -3x3ex Find the first derivative of the above function.

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Q: Q2/ Find the derivative of the function f(x) V4-x2 by definition

A: The derivative of a function f(x) with respect to x is given by limh→0fx+h-fxh. The given function…

Q: Given f(x)=√x + 3, find f'(-2) using the definition of a derivative. Provide your answer below: ƒ'(…

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Q: function with respect to x. a. f(x) = -4x – 2 b. f(x) = 3x² + 4 c. y = 3x² + 3x + 3

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the derivative of the function. g(x) = 4e√x g'(x) =

A: Consider the given function:

Q: Find the derivative of the function. t(x) = x2 − 8x3  / x

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Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

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Q: b) f(x) = (e* (Inx² – 3))*

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Q: Given f(x) = 2, find f' (1) using the definition of a derivative. x-2 Provide your answer below:…

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Q: Find the derivative of the algebraic function.

A: Given algebraic function fx=3x-1x. Differentiating the given function with respect to x,…

Q: Using the definition of derivative, find the derivative of f(z) = x + 5x + 5. %3D

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Q: Use the appropriate Derivative Formula for the algebraic function below. x2+1 2. y = x2-1

A: y=x2+1x2-1In this we use quotient rule QUOTIENT RULEy=uvdydx=v.dudx-udvdxv2apply this rule in given…

Q: Compute the derivative of the given function in two different ways. x3 + 4x? h(x) = 5x2 g• f' – ƒ ·…

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Q: Find the derivative f'(x)=? of the function f(x) = 2x5 +√√x -+ 2x - 3

A: SOLUTION-

Q: Find the derivative of the following function by applying the definition of the derivative. State…

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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: Using the second derivative criterion, find the graphs of the functions b) F(x) = x³/3 - 9x + 3

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Q: B2(a): Using the definition of derivative, find the derivative of f(x) = x² + 7.

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Q: Q2/ Find the derivative of the function f(x) =V5- x2 by definition

A: →When limit is of the form 00or∞∞ (Indeterminate form ) then L Hospital's rule is used . In this…

Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

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Q: a) Use the definition of the derivative to find f '(x), given f(x) = 4x² – 1.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the derivative of the function f(r) = 3x² – 12x by the definition of derivatives | f(x +h) -…

A: here option C is true 6x-12