1, Differentiate the function. (2) f(x)= 5x² – x+1 (3) f(x)= (2+3x'j - nx (4) f(x)= e (5) f(x)= (x³ +1)°(2x² – 3)³ (6) f(x)= x'e$*r

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Q: 41. What is the derivative of f(x) = secx + 3 csc x? A. f¹(x) = sec xtanx + 3cscx cotx 3cscx tanx C.…

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Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

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

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

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

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A: We use the limit definition of the derivative

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

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

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

A: Given function is

Q: Q.2 Find the derivative at each critical point and determine the local extreme value. (a) y=x√√4x² 1…

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Q: The maximum value of y = cos x for - < x< is 1

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Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Determine the first derivative of the ff. function a. y = 400(2)**3 sin 3x b. y = Vxe2* cos x…

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Q: maximum point of y x – 2

A: Condition for Extreme Value: A continuous function fx, y has extrema at a, b if fx=fy=0 at a, b…

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A: Given function is By limit definition of the derivative

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Q: Compute Anti-Derivative (-1 --> 1)  (x^3 + x) / (cos(x) + pi) dx

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Q: 8. Find the Laplacian of Ø = xy²z³

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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

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

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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: 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: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

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

Q: How do you find the partial derivative of a given function using the definition formula?

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Q: 2. Find the critical points of f(x, y) = x³ + 2y³ – xy and analyze them using the Second Derivative…

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Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

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A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

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Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = 1+8x - 3x2

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Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2x2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

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Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

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Q: 1. Show a numerical method of approximating the instantaneous rate of change at x = 3 for the…

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Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

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A: Given: A flexible stretched string is constrained to move with zero slope at one end x=0, while the…

Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…