Find and simplify the difference quotient f(a + h} – f(a) for the function. (x) = 5Vx

Q: use the Product Rule to calculate the derivative. f (x) = (3x − 5)(2x2 − 3)

A: use the Product Rule to calculate the derivative. f (x) = (3x − 5)(2x2 − 3)

Q: For the function f(x) = 4x- 3x +2x +6x +2, find f"(x), the third derivative of f, and f''"(x) = %3D

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Q: Find the slope of the secant line to the function f(x)=x3 when x=1 and x=2.

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Q: Use the chain rule to find the derivative of f(x)= 4(2x^3−4x^9)^12  f'(x)=_______

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Q: Use the chain rule to find the derivative of f(x)= 5e^-9x^3-6^x^7

A: Given query is to find the derivative of the expression

Q: Use the General Power Rule to find the derivative of the function. 4 g(x) (5x² + 3x)7

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Q: Find the derivative of the function, f (x)=(3x-2)° (2x+5)

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Q: Use the chain rule to find the derivative of f(x)=5(6x^6−5x^10)^19 find f'(x)

A: Chain rule: According to the chain rule derivative of y = f(g(x)) is given by:

Q: For the function f(x)=2x^3-12x^2+20, Use the SECOND DERIVATIVE TEST to find the relative extrema.

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Q: Use the chain rule to find the derivative of f(x) = 4/2x° + 7x7

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Q: find the derivative of f(x) = x2 – 3x + 4, and then 3) evaluate f '(2)

A: Given : f(x) = x² - 3x + 4

Q: For f(x) = (2a* + 3x)(5x*), find the derivative of f(x). 80x7+ 60x3 20x7-30a3 O 10z8 + 15x4 O…

A: We will use concept of differentiation to solve this.

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

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Q: For the function f(x) = (5x² − 2)4 determine the second derivative in factored form.

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Q: Find the derivative of the function f(x) (3x+6)? 6x2+13

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Q: Find the derivative of the function. r (x) = 3x 20.6 8. -8 - 6. 6x1.6 2]

A: The derivative of a polynomial function with degree n:

Q: Find f'(x) using the rules for finding derivatives 5x2 - 9x +2 f(x) = 7x + 1 f'(x) =|

A: The given function is  f(x) = (5x2 - 9x + 2)/(7x + 1)

Q: find the derivative using the definition g(x) = 2x2 + 1

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Q: For the function f(x) = 5x° - 3x + 2x + 7x + 3, find f"(x), the third derivative of f, and f4) (x),…

A: Third and Fourth derivative of f(x): f3x=300x2-74x+12f4x=600x-74

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

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Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

Q: Given f(x) = -x² – 4x – 6, find f' (4) using the definition of a derivative. Provide your answer…

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Q: calculate the derivative. f (x) = 4x5/3 − 3x−2 − 12

A: To find the derivative of: f(x)=4x53-3x-2-12 Solution: f(x)=4x53-3x-2-12 Differentiating both sides…

Q: Use the chain rule to find the derivative of f(x)=3e^−4x^9+3x^3   f'(x)=

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Q: Find the derivative. a) (x-3)(x+2)(x^3) b) 9x^2(10x+4)

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Q: Given f(x) = –3x² – x + 15, find f' (-3) using the definition of a derivative. Provide your answer…

A: f(x) = -3x2 -x +15 find f-1(-3)

Q: Use the Quotient Rule to find the derivative of the function. 3x - 7 g(x) = %3D x² - 1

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Q: Find the derivative of the functionf(x)= 9x² + 4x +6, using the definition of the derivative,

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Q: f(2) — V3х — 7

A: Solved using terms of derivative.

Q: For the function f(x) = 3x- 4x +3x +5x +6, find f'"(x), the third derivative of f, and f(x), the…

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Q: Given f(x) = 5x² + 5x + 2, find f' (x) using the definition of a derivative.

A: Given function is solved through derivative  detailed solution is given below

Q: Find f'(x) using the rules for finding derivatives 4x2 - 7x +6 f(x) = 2x + 1

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Q: Calculate the derivative. f (x) = 4x5/3 − 3x −2 − 12

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Q: Find the derivative of the function. f(x) = (2x3 - 8x² + 3)4 %3D

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Q: Find the derivative f(x)=2x^5(√2x^5+5x^4)

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Q: Use the Product Rule or the Quotient Rule to find the derivative of the function. f(x) = (6x² +…

A: Given,         F(x)=(6x2 + 9) ( x2 - 5x - 8)

Q: Find the derivative of the function. g(x) = 8/ (5x2-6x)4

A: To find the derivative of the function

Q: Find the derivative of the function. F(x) = (x4 + 5x2 – 9)6

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Q: Use the chain rule to find the derivative of f(x) = 2e5a* + 9x³ %3D f' (x) =

A: We have to find

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

A: SOLUTION-

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

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Q: Find the derivative using the definition for the function f(x) 4 +8x-5x2.

A: Limit defination of derivative f'(x)=limh→0f(x+h)-f(x)h

Q: Use the Product Rule to find the derivative of the function. f(x)= (4x+ 7)(x² 8) а. 8х b. 2x + 4 c.…

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

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Q: For k(x)=(−3x2+2x−3)(x−2)(−x+3), find the derivative of k(x) using the product rule.

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Q: Find the derivative of the function. f(x)=6x2(9-8x)4

A: Use the product rule of differentiation: fx=ux.vxf'x=u'x.vx+ux.v'x

Q: Use the Product Rule to find the derivative of the function. f(x) = (5x − x3)(9x + 8)

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Q: Use the definition of the derivative to find the derivative of f(x) = x² - 2x + 7

A: By the definition of the derivative f'(x) = lim(h tends to 0) (f(x+h)-f(x))/h

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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