Suppose that f(x) is a differentiable function such that f(3)= 8 and f'(3)=-2. If g(x)=xf(x), then what is g'(3)?

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

A: Given,

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

A: We have to find derivative of the function using limit process: fx=x+4 We know the formula of…

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Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: FIND THE DERIVATIVE BY THE LIMIT PROČESS OFF(x) = Vx+2.

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

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: Find the derivative of the function by the limit process. f(x) = √(x + 4)

A: Given function is

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y…

A: d2dx2arctan3x-44=d2dx2arctan3x-42=ddx1x3x-4=-9x-82x23x-43x-4…

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Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

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Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

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

A: Given: the function xfx, where f is a differentiable function of x.

Q: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: 2) Let f(x) = x' +x² – 5x – 5. Use the second derivative test to classify the critical points.

A:

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

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

A: The given function is fx=-5x. Obtain the derivative as follows.

Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

Q: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: Find the derivative of the function by the limit process. f(x) = 5x − 4

A: fx=5x-4

Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

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Q: Use forward, backward and central difference approximations to estimate the first derivative of:…

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Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

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Q: 2. use the fundemental derivative formula to differential the folwing at x=2 • gex) = 3x-1 2メ+1 (1o…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find the derivative of the function by the limit process. f(x) = 1/x2

A: Here the given function The first derivative of function f(x) is defined by limit prosses as

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A: Solve the following

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A: Given the first derivative is: y'=6x+1x-22

Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

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Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

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

A: Given: fx=x2-5 To Find: The derivative of the given function by the limit process

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

A:

Q: Find the derivative of the function by the limit process. f(x) = 3x- 1 - (x), J

A: fx=3x-1

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A:

Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

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Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: Find the derivative by the limit process. f(x) = 13 – x2

A: Given that: f(x)=13-x2

Q: Find the derivative by the limit process. f(x) = 15 – x²

A: Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

Q: If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.

A: Now the derivative of a function f at a point 'a' is given by,

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A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

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

A: