Find a linear approximation to f(x) = 4xe2*-6 at x = 3. Use this linear proximation to estimate the value of f(3.1) and f(2.98).

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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Q: Find the directional derivative of the following function at P(1, 0) in the direction that produces…

A: Given  fx,y = -3x2+4y3+2xe32y

Q: Find the derivative of the function f(z) = (3x +1)In(4x+3) %3D and then evaluate it at x = 0. f' (0)…

A: Given : f(x)=(3x+1)ln(4x+3)

Q: At what time does f (t) attain its largest value?

A: Consider f(t) is any function. We know that function attains its largest or smallest value when the…

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: 2 -

A: Chain Rule : (fg(x))' = f'(g(x)).g'(x). d(ax+b)ndx = n.a(ax+b)n-1 dtanxdx = sec2(x)

Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

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Q: Use the u-substitution to find the anti-derivative of m'(x)= 1/xln(x)

A: solution :- antiderivative is the integration  So put ln(x)  = u Then (1/x )dx  = du And then…

Q: What is the approximate derivative of f(x) = x²ex, using backward-difference approach at x=2 and a…

A: The formula for the backward difference is f'x=fxi+1-fxih Now, h=0.1xi=2xi+1=xi+h=2+0.1=2.1fx=x2ex

Q: Let f(x) = -4 + (2x – 15) In(3/x – x + 5) %3D (a) Find the derivative of f. (b) Using the derivative…

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Q: Use three-point midpoint formula to evaluate the first derivative of y = x² + 4x − 5 at x = 0 using…

A: The given problem is to find the first derivative of the given function at x=0 with given h value by…

Q: Solve for the 2"nd derivative of the function f (x) = 3x5 – 4x3 + 7x² – 10. a. 15x* – 12x2 + 14x b.…

A: Given: fx=3x5-4x3+7x2-10 To Find: 2nd derivative of the given function

Q: 2. Given: y = f (x) = (2x-2 + 5x³). What is the slope (gradient) of the first derivative function at…

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Q: Find the second order derivative of ycos³(2x).

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Q: Use the second derivative test to identify any critical point and determine what each critical point…

A: Critical point: The point where the function fx, y is defined and its gradient is a zero vector or…

Q: Find the derivative of the function 3 f(x) = V (x² – 2)' at x = -1. f'(- 1) =

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Q: Find the derivative using the definition. a. f(t) 2t+1 b. g(x) = 2x² +1

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Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: Find the linearizationsof the following functions at x = 0. ex

A: fx=ex at x=0. Now differentiating with respect to x, we get f/x=dexdx=ex Now, f0=e0=1 & f/0=e0=1

Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

Q: Q2/ Find the derivative of the function f(x) = V3x +1 by definition %3D

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Q: Q2: - Find the second derivative of the following function at x = 2 15 marks 1) y=+ V 2) y 3 (x +)…

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Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

Q: find the most general anti derivative  f(x) = e^2

A: A function F(x) is called an antiderivative of f(x) if F’(x) = f(x).   The function f(x) is the…

Q: Find the derivative of the function. F(x) = In(4 – x®) %3D f'(x) %D

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Q: Find the actual error when the first derivative of f (x) = In x at x = 2 is approximated by the…

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Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

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Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

Q: Find the actual error when the first derivative of f (x) = In x at x = 2 is approximated by the…

A: given  fx=lnx f'x≈fx+h+2fx-3fx-h4h to find the actual error

Q: Find the approximate value of second derivative f"(0) with the step h for the following function by…

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A: Explanation: The given function is: f(x)=-3xx+1 Find the first derivative of this function.…

Q: Find the indicated derivative.dp/dqfor p =q2 + 2/4q-2

A: Given a function in p in terms of q as shown below. We need to compute dp/dq.Here we use (u/v) rule…

Q: F(x)=In(52x+n • (x+2) ) %3D

A: Find the derivative of the function

Q: Find the derivative of the linear fractional function y=ax+bcx+d.

A: We have to find the derivative of    y=ax+bcx+d ddxy=ddxax+bcx+dWe have to apply division rule…

Q: Find the derivative of the following using the three-step rule Зх-1 1. у3D 2x+5 2. y=Va² +x²

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Q: The derivative of y x²+1 is х2—1 =

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Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: %3D

A: Formula:ddx(tan x) = sec2xddx(ln x) =1xddx(xn) =n xn-1

Q: Find the derivative using the long method 3 u = t2

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Q: Find the given flx), + 2x derivative of function. %3D a+x

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Q: Consider the function f(z) = V1+z -1 and find its derivative:

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Q: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

A: Derivative of the function using definition

Q: Find the second derivative of vx - Jy= 4 when x = 1. 2 1 -1 -2

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Q: Use the sign pattern for the derivative dƒ/ dx = 6(x - 1)(x - 2)^2(x - 3)^3(x - 4)^4 to identify the…

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Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

Q: Find the derivative df/dt. * f (t) = 2' + In (t)

A: Given f(t)= 2t+lnt

Q: Find the derivative of the function. f(x)=4tan-1(e9x)

A: Consider the given equation

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

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Q: a) Find the derivative of the function: T+ V3x f (x): 3x-1

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Find the derivative of the function. g(x) = [*- 1 -dt -5 2+4 10 а. 841 b. 2x (x²+ 4)² 1 С. x²+4

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;