1. Use the following formula (1) to evaluate derivative for each of the functions below: f(x+ h) - f(x) f'(x) = limh¬o (1) h (a) f (x) =VT+ 3x + 1

Q: If ƒ(x) = x^n, n>=1, show from the definition of the derivative that ƒ′(0) = 0.

A: Given,

Q: Solve the first derivative of f(x) = e-2x In x at x 0.5 using forward finite-divided difference and…

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

Q: 1. If y = x³ + x - 5 then what is the derivative of y with respect to x?

A: Derivative of a function

Q: Find the derivative of the function.

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Q: 2. g'(x) where g(x)= x² +7x-5

A: differentiation by using first principle

Q: 1. Find the derivative of each of the following functions using chain rule: y=3x* (x* -2) a)

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Q: Find the derivative of ywith respect to x in the following functions: 18x y (ans.: (3x-2 a) y= and…

A: Derivative of uv uv' = u'v-v'uv2

Q: Find the derivative of the following functions using the long method (limits) (a) x =t-5t- 3 (b) y =…

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Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

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Q: Let f(x) x + 1 Use the limit definition of the derivative to find the slope of the line tangent to…

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Q: Find the first derivative of y with respect to x for the following :functions b- y = In( 3x .e-*)

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Q: 1. Use the definition of the derivative to find the derivative of the following functions. 1 (b)…

A: use definition of derivative to find the derivative of the following functions a) fx=x+2 it is known…

Q: Suppose that f'(0) = 2. Find the derivative of the function (e2z – 2x)f(3x) at x = 0.

A: Given that f'(0)=2.Our Aim is to find the derivative of the function (e2x-2x)f(3x)-(i) at x=0.

Q: Find Find the second derivative of the given function. y = In(x² – 1)

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Q: Defermine the derivative of the following functions using the long method (using limits). 1. y =t –…

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Q: 1 y = V2x+5 /2х+5

A: By see this solution

Q: Solve the first derivative of f(x) = 52x+1 at x = 0.5 using backward finite-divided difference and a…

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Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

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Q: 1. f(x) =In (ta n"x)

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

Q: Find the derivative of the following function using the limiting process. f(x) = 1/x2

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Q: Find the derivative with respect to x of 1 f(x) V3x + 9

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Q: Find the derivative at the given point. f(x)= at x = 0 %3D x+1 O 1/4 O-1

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Q: Let ƒ(x) = √2x + 1. Compute ƒ'(2),the derivative of ƒ at x = 2, and use the result to find an…

A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In(In 9x)

A: The solution for the above question is as shown below.

Q: 15 - What is the approximate derivative of f(x) = 5x° + 4x? if we use forward difference method,…

A: Derivative of function at any point gives the slope of tangent to the function at that point.…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: Find the derivative of function defined as follows. h(x) = (x2 - 1)3

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x y = In (x + 2)5 4x - 7 (x +…

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Q: 3. The derivative of f(x) = In x at x = 3 when h = 0.002

A: 3) To find the true error and relative error of the function: f(x)=ln x, x=3 & h=0.002

Q: In (6x) Find the derivative of y with respect to x if y = sin (3e) dt.

A: the given function is: y=∫0ln(6x)sin3et dt we have to find the derivative of y with respect to x.…

Q: 19.What is the derivative with respect to a of f(x) = 4-32 3z+2 4x-3

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Q: If y = cos x, then the nth derivative of y with respect to x is equal to itself if n is a natural…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Suppose h(x): . What is the correct result of the derivative of h with respect to x? 3x · In (5)…

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Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

Q: Find the function with the derivative f'(x) 3x = e whose graph passes through the point P| 0,

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Q: 5. a) Find the first order derivative of the following function. y x° In x

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 2. Find derivative of given function defined as follows 2x y = e = ²

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Q: In (4x) Find the derivative of y with respect to x if y = sin (8 e') dt.

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Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

Q: 1. y = cos2(2x − 1)

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

Q: Q3: find the derivative of the following: 1. y = Inx + √√1-x² sech-1x

A: I have given the answer in the next step. Hope you understand that

Q: Compute the second derivative with respect to r of 3x + 8 y = at x = 1.

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Q: Prove, by Showing all steps i that the 1. derivative of arcos x is 1-メ

A: Derivative of arccosx is -1/√(1-x2)

Q: Suppose the derivative of the function y = f(x) is y' = (x-9)2(x+6). At what points, if any, does…

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Q: 2. Find the derivative of h with respect to u if h = n²u

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Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

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Q: Monday, 1) Find the derivative of the given function with respects to e y = 3lan® In 3

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Q: Зх +1 a) y =- 1 b) g(x)= Jx -

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Q: Find the derivative of the following functions by applying "Delta Metho Show your complete solution.…

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