(X),4 %3D (b) Compute the derivative of f(x). (g) 4 (x)J – (4 + x) 10xh + 5h“ – x + 8 8 + x – 2. (a) Compute the difference quotient of f(x). %3D Let f(x) = 5x² + x – 8. Y NOTES

Q: -What is the derivative of (x + 1)2 ? a) x? + 2 b) x c) x d) 2x+2

A: We will use chain rule of derivative

Q: Q-1- Find the derivatives of the functionS 1- Y+In (xy) = |

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Q: 9. Find the first derivative: f(x) = 3ex %3D x2 (x+1)

A: Derivative of function

Q: Find the derivative of y with respect to x. 4. (x² - y²)² = 4ay²

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Q: Determine the derivative of y (x) = ( 3 x² + 11 x + 4 )³ e-6 x with respect to x. y '(x) =

A: topic - derivative of a function

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: Find the derivative with respect to x if f(x) = e -14x The derivative with respect to x if f(x) =…

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Q: f(2o+h)-f(x0) h 7- What is the approximate derivative of f(x) = 5x³ + 4x² if we use forward…

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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: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

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Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (2) — 5а — 4 %3D | 2. f…

A: Recall: Derivative using Four step Rule:step 1 : Write f(x+h) and f(x).step 2 : Compute f(x+h)-f(x)…

Q: a) Find the derivative of g(x) = 3tanx – 4cotx. %3D b) What is the value of g 3.

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Q: 4. Find the derivative of the following by applying the chain Rule and simplify. a. f(x)=| x+3 b.…

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Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: 4 Find the derivative of the function y= f(x)= Jx(x-8). %3D

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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: V². Find the derivative of f(x) = In x² +1 %3D x(2r - 1)2

A: Derivative: f(x)=lnx2+1x(2x3-1)2ln(mn)=ln m-ln nln(x2+1)=12ln(x2+1)

Q: Find the derivative of y with respect to x. 8x y = tan 3 - 24 O A. 64x2 + 9 O B. 64x2 + 9 24 Oc.…

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Q: 13. In y = what is the derivative of 2x2 +3? x+1 a) 2x b) 4x c) 4x +3 d) 7

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Q: Q. / Find the derivative of y = (In(x²))'n(x²).

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Q: Compute the derivative function f'(x) algebraically. f(x) = 8x – 5 %3D f'(x) =

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

Q: Find the derivative of the function f(x) = – 2x1 + 5x – 7. A. -2x + 5 C. -2x? + 5 E. None of these…

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Q: What is the derivatives of f(x)=(x^3)/(9-X^2) and its x and y intersect?

A: a) From the given problem: fx=x39-x2Ory=x39-x2   So,   dydx=ddxx39-x2=ddxx39-x2-ddx9-x2x39-x22…

Q: What is the derivative of y = (x2 + 1) e-3 ? O y = (x² +1) (e-3) + xe² - 3 O y = (x² +1) (e*-3) +…

A: It is required to find the derivative of the given function.

Q: 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1)' %3D c. f(x) = 4e*- x %3D

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: 2. Find the derivative using chain rule. (a) f(x) = 5(2.r + 3)3 Answer: (b) f(x) = (x - 4)*(2x +3)…

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Q: Find the derivative of the following using the three-step rule Зх-1 1. у3 2x +5 2. y=Va² +x?

A: Using three step 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: 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: The derivative of y x²+1 is х2—1 =

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

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: What is the value of y' at x=-4 is ______? Evaluate the derivatives of the given function for the…

A: The function is given by y = 5x2-x+53-3x-x2 To evaluate : The value of y' at x =-4

Q: Find the derivative using the definition fex)- = C fcx) fCx) = そり f ex) = KX" f cx) fx) = gx).hcx) 9…

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Q: 2x Find the derivative of h(x) 2x + 3

A: Given:  Function  h(x)=-2x2x+32

Q: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

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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: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

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Q: 2. Find the derivative of (a) f(x) = x* + 4x 2 + 4e" (b) f(x) = 2 tan (x) – 6"

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Q: Find the derivative of f (x) = coth³( In(x³)). -9coth (In(x³)) csch²(In(x³)) A B - 9x?coth ( In(x³))…

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Q: Compute the derivative function f' (x) algebraically. f (x) = -5x3 +7 O f' (x) = -15x O f' (x) =…

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Q: Suppose =V1+ Vx. What is the correct result of the derivative of g with respect to x? A 8'(x) = 2/1+…

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Q: 4. The derivative of the function f(x) = r +3) is

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Q: 2. Determine the true error and the relative true error of the first derivative of f(x) = 2.5-* %3D…

A: Solution is below

Q: 2. Consider the function f(x) = e¯*. -2x (a) Show that the derivative is f'(x) = %3D

A: