II. Use the limit definition of the derivative to find the derivative of the function. 1. f (x) —D х2 — Зх + 1 2. у %3D у3х — 2 y = - 3 3. g (x) = V2x-1 1 4. h (x) x3 ||

Q: • Find f (x) of f(x)=by using the definition of the х-1 derivative. • 1- Find if y=3t-4 and t = Vx +…

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Q: 1. Find the derivative using chain rule. (a) f(x) = (x5 – 2)20 %3D Answer: (b) f(x) = V3r² + 1 %3D…

A: Since you have posted a question with multiple sub parts, we will solve the first three subparts for…

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: 4. Determine the derivative of the function with respect to x. 8sin?(x² + 2) y = 4tan²(x² + 2)

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Q: 1. Determine the first derivative of the functions below with the rules for deriving the function:…

A: A Given function is y=4x3+32. Use formula ddxxn=nxn−1 Differentiate  y=4x3+32 by using the chain…

Q: 4. Find the derivatives with respect to x of the function 2 – 3x^2. 5. Differentiate ax² + b to the…

A: Using derivative of composite function.

Q: 4. Consider the function f(x) = Vx – I (a) Use the limit definition of derivative to find f'(x)

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Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: II. Obtain the required order or level of derivative. 1. y = 3x5 + 4x³ – 4x + 1, find y" 2. f(x)…

A: Solve differentiate

Q: B. Find the derivative of the function. 1. y = 3 2. f(x) = x + 1 3. f(t) = -2t + 3t- 6 4. f(x) = x?…

A: Since you have posted question with multiple subparts, here is the solution for the first three…

Q: 6. Determine the derivative of the following functions. Do not simplify. (a) y = 2t° +t+ e² 2 (b) y…

A: Given:           (a) y=2t5+t+e2Differentiating with respect to…

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 1. Let f(x) = mx + b, the line with slope m and y-intercept b. Use the rules of differentiation to…

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Q: 10. Iff(x) = Vx find f (4). 11. Use the limit definition to find the derivative of f(x) = x² –2 x.…

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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: What is the derivative of y + x + y² = x ? O y : 1- 3z2 3y2 + 2y 1+ 3x? 3y? + 2y O y = 1- 3x2 3y? +y…

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Q: 4. Consider the function f(x) = Vx – 1 (a) Use the limit definition of derivative to find f'(x)

A: Ans:- Consider the function f(x)=x-1(a) we have to use the limit definition of derivative to find…

Q: A) Find an equation of the line tangent to the function of x2 + (y – x)² = 9 at x = 1. dy 3) Using…

A: A).Givenx2+(y-x)2=9(y-x)2=9-x2y-x=±9-x2y=±9-x2+x -----{1}Taking positive of equation {1}y=9-x2+xNow…

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

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

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Q: 20. Find the derivative of the function. y = 9cos(2x) a. y'=-18sin(2x) b. y' =18sin(2x) c.…

A: Option (a) is the correct option. Differentiate y using the chain rule.…

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

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Q: Find the function with derivative f'(x) = e8 that passes through the point P= (0,7/8).

A: We are given a diierentrial equatrion[f'(x)=e8x ] and a pssing point (0, 7/8) of the same  we need…

Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

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: Consider the function f (x, y) = x²y³ – 3xy³. Compute the value of the derivative frvy at the point…

A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

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Q: B. By using the definition of the derivative, find the for: dx 1- f(x) = V %3D 2- f(x) = x -!

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Q: • Find f (x) of f(x)= by using the definition of the x-1 derivative. • 1- Find if y=3t-4 and t Vx+…

A: we have to find the derivative using definition. as per definition  f'(x)=limh→0f(x+h)-f(x)h

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: 3. Find the derivative of ywith respect to x in the following functions: 18x y (3x-2 + 4x) x'- 3 a)…

A: Please see the explanation below

Q: 4) Find the following derivatives using derivative rules, not the definition. a) f(x) =x -3F+5

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Q: Q1) The dervative of the function f(x)= |x+2 using the definition of derivative is

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Q: Find the derivative of the given function.   f(z)=−1/z^4.1

A: Recall the rule for differentiating powers when the exponent is a positive integer

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: To find a linearization at a suitable chosen integral near a= 0.11 at which the below function and…

Q: (a) Find the derivative of y = f(x) =2x+1 using this definition f (x+h)-f(x) f'(x)= lim h (b) If x…

A: Differentiate above function with respect to x

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: To determine the linearization for the function.

Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y- x)² = 9 at x = 1. dy if y =…

A: Derivative of function

Q: 6. Use the limit definition of derivative to find f'(x) for the functions below. (a) f(x) = /4r – 1…

A: limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

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Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

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Q: 2. Find the derivative of (a) f(x) = x* + 3x 2+ 4e" 4 (b) f(x) = 2 tan(x)- 2"

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

Q: If g(z) = 6z-2), then its derivative is given by:

A: For simplification, take natural logarithm on both sides of the equation gx=6x2-2 and apply the…

Q: 2 Find the derivative of the following function f(x)=2x-10x -8 using the limiting process a.…

A: The function is given by f(x) = 2x2-10x - 8 To evaluate : The derivative of the function using…

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

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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: Find the function with derivative f'(x) = e7¤ that passes through the point P = (0, 6/7).

A: Given that f'(x) = e7x and we find function that passes through point (0,6/7). We know that f'(x) is…

Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

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

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