Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0). Assume also that f(2) = -13 |f(x)| < x³ + 9 and 5 Determine the value of -x/5

Q: Determine the derivative of f(x) = 3 x2 In x with respect to x. f '(x) :

A: We differentiate both sides with respect to x and apply the rule d/dx(uv)=ud/dx(v)+vd/dx(u)

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Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

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Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

A: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x²-6x+5.

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Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x³-8x+9.

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Q: Find the derivative of: f(x) = (x3 + 2) In(x)

A: Consider the function

Q: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

Q: Give an example of a function f (x) that has one  positive derivatives on the range (−1, 0) and a…

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Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

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Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: 8. Find the derivative of f(x) = (1+x³)' ( 14x + - ) using differentiation rules.

A: topic - derivative of a function

Q: 7) f(x) = 3e In x %3D

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Q: Use the definition of a derivative to determine all points for the function f(x) = ((x+|x|)^2)+1 is…

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Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

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Q: y = x*(1 – In x4)

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Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: Find the derivative of the function using Chain Rule. (2x-6)-¹ (x²+3) h(x)=

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Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

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Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

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Q: 3) Find the derivative f(x) = xe-*In(x³) %3D

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Q: Find the derivative using the limit process of f(x)=x² + 3x f(x)=x² +3x

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Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: Find the relative extrema of the function f(x)= x2+3x+4 using first derivative test.

A: fx=x2+3x+4 To find extrema of function.

Q: Find the derivative of f(x) = 6* – 3* + In x -

A: Differentiate: fx=6x-3x+lnx

Q: 1. Find the derivative of f(x) = 3x³ + 2x using the limit definition.

A: We have to find derivative using definition.

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Find the derivative using the first principle  F(x)= (x-1)(x-2)

A: Given F(x)=(x-1)(x-2) To find the derivative using the first principle From the first principle, we…

Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

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Q: 3 Determine the 3rd derivative of the function f(x) = 2√√x-x³

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Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

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Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 3

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Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

Q: :) Given f(x) = |x|+x, at which point does the derivative not exist? Mathematically Question 4 (-…

A: We are given a function fx=x+x and we have to find the point at which fx is not derivable. We know…

Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f'…

A: Use differentiation of trigonometric function

Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: Find the x-value for all relative extrema of f(x) using the first derivative test, and specify…

A: f(x)=x3/3 + x2/2 -2x Find the x-value for all relative extrema of f(x) using the first derivative…

Q: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

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Q: 2x 3, Use the limit definition of derivative to show that f(x) is differentiable at x2 – 3, r > 2 x…

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Q: Find the relative extremum of g(x) = x - 3x +1 by using first derivative test.

A: Let g(x)= x3-3x2+1 To find the relative extremum , here we use first derivative test In this method…

Q: find the derivative of f(x)=x/(x+2) using the limit definition of a derivative

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Q: Find the derivative of the function.

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Q: Find the local extremes of f (x) = x³ +2x+ using the first derivative test.

A: Given,         The local extremes of fx=x3+34x4 using the first derivative test.

Q: Find the derivative of the function by the limit process. f(x) = 5 − 2/3 x

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Q: 1. Use the definition of the derivative to find the derivative of f(x)- V-x-2

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Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A: Given :   f(x)=x4 , at x=3/2 f(x)=1/4 , at x=2