Develop a general rule for the nth derivative of xf(x), where f is a differentiable function of x.

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 1 12. f(x) = 3…

A: Functions are given, we have to find the derivative at the given values.

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)

Q: 1/x using the definition o

A: we have to find the derivative of f(x) using the first principal. f(x)=x+1x

Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

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Q: Define the derivative of f(x) at x

A: Consider a function f(x) The differentiability of a function:  Let f(x) be a real valued function…

Q: Find the derivative of f(x) = x2 using the limit definition of derivative.

A: We have given function  f(x)= x2 So using definition of derivative  f'(x) = limh→0fx+h-fxh So,…

Q: Find the derivative of the function by using the rules of differentiation. 1 f(x) = f'(x) =

A: topic - derivative of a function

Q: Prove, using the definition of derivative, that if f(x)  = Cps x,then f'(x) =- Sin x

A: Given fx=cos xBy definition of derivativef'x=limh→0 fx+h-fxhfx=cos xThereforef'x=limh→0 cosx+h-cos…

Q: 2 f(x) = ; 2x-1

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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: Topic:- calculus

Q: Calculate the derivative of f(x)=4x³ with respect to x and evaluate this derivative at x=2.

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Q: Determine the derivative of the following function by applying the quotient rule.…

A: The given function is: h(x)=ln (x2+x)x2+1 The quotient rule for the derivative is given by:…

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: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: Find the derivative of F(x) = 1 / (3x+1) directly from the definition of the derivative:

A: Here the question itself need to use definition of derivative to find out the derivative of given…

Q: Use the following definition of derivative as a function f\x+h}-f(x) f\x)=lim h h --0 To find the…

A: A function is: a relation from a set of inputs to a set of possible outputs where each input is…

Q: Find the derivative of the function by the limit process.

A: Consider the given function fx=1x2   Derivative of any function fx using limit process is…

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) at the designated value of x (Using Derivative Rules). 3 11. f(x) = 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: Find the derivative of the function. 8x f(x) = In f (x) =

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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: By using the limit definition of a derivative, determine the derivative of f(x) = 1/x at x  = 2

A: By using the limit definition of a derivative, determine the derivative of f as shown below:…

Q: Find the derivative of the function using the definition of derivative. f(x) = rx + q

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Q: Find the derivative using the definition of the derivative for f(x) = Vx (ie. f'(x) = fn &+h)-{(x) ,…

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Q: Find the derivative of the function. f(x) = In(x + V2 + x²) f '(x) =

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Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: find the derivative of f (x) at the designated value of x. f (x) = x + 11 at x = 0

A: To find the derivative of f(x)=x+11 at x=0 Solution: f(x)=x+11 Differentiating both sides w.r.t x we…

Q: Find the derivative of the function. f(x) = (x2 + 3) In(x) f'(x)

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Q: Use the limit definition of the derivative to find the derivative of f(x)=x^2+x

A: Please refer the attached image for complete solution.

Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

Q: f(x) = x In x

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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: 3) Find the derivative of the function f(x)= x² –x+2 using the definition of the derivative (a…

A: Given:     To determine: Derivative of the function using the definition of the derivative.

Q: Calculate the derivative of the function below using the quotient rule. x4 y = Vx + 2x4 f(x) = and…

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Q: Use the limit DEFINITION OF A DERIVATIVE to find the derivative of the function. 16) f(x) = Vx + 5…

A: The derivative of a function y=f(x) is given by f'x=limh→0fx+h-fxh. The given function is fx=x+5.

Q: Use the General Power Rule to find the derivative of the function. g(x) = V2 – 7x g'(x) = %3D

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Q: Use the General Power Rule to find the derivative of the function. g(x) = V7- Sx

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Q: Find the derivative of the function. f(x) = In x+ 2 f'(x) =

A: We have to find the derivative of the given function.

Q: Find the derivative of f(x) = x cos x using the product rule.

A: The given function is fx=xcosx.

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

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

A: According to question given that f(x)=|x|+x"A function f is said to be differentiable at a if  f'(a)…

Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

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Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

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

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Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: What is the derivative of f(x) = 1 over x⁵

A: here we use the formula of derivative  ddxxn=nxn-1

Q: Find the derivative of f with respect to x of f(x) = In x'

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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