Q5.Find the first and second derivatives of the following functions with respect to the given variable: i. f(x) — 2е-2х ii. g(t) = (1 – t²)³ | и iii. h(u) 2и+1

Q: Find the derivatives of the function x²(xy² y)² = x² - y² )

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Q: У y = |1 - х - 1+х

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Q: Find the derivative of the function f(x) = 4v3x² – x. 12х - 2 A. V3x2-1 6х - 2 бх — 1 C. V3x2 –1 E.…

A: To find the derivative of f(x)=43x2-x

Q: 1. Find the first derivativ

A: Given that,

Q: 14. What is the first derivative of f (x) = (x²- 4)(3x - 2)? %3D a. 9x2- 4x – 12 С. 6х d. (x + 2)(x…

A: first derivative of f(x) = (x2 -4)(3x-2) f(x) = 3x3 -2x2-12x +8 now df(x)/dx = 9x2 -4x -12 so answer…

Q: 2 Find the second order derivative of the following functions y = f(x) and evaluate them at x = 2.…

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Q: The derivative of the following function y=(x - 3) ( 1– x) O 4+ 2x O 4- 2x O 2+ 4x O 2- 4x

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Q: Determine the second derivative of y = V5x² + 1 Determine the third derivative of y = (x² – 1) (2x³…

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Q: 1. x³ + y³ – 3axy = 0 2. x2 - 2xy + y? – 6x + 2y = 0 3. (x+y)2 2ay 4. x + yi = 9| 5. (x² – y?) =…

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Q: 2. Find the first and second derivatives. Simplify as needed. (a) f(t) = t sin t )=-=- (b) h(r):

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Q: Find the first and second derivatives of the following function: g(t) = t°et g'(t) g" (t) =

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Q: f (x) = x³ + 4xª + 3x³ – x² + & 1. ,2 -

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: 12. a(t) a' (t) b(t) b'(t) -4 2 -3 -4 1 a. f(t) = a(t)b(t) Find f'(-4). b. g(t) = -3a(t)b(t) Find…

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Q: I. Find the derivatives of the following functions: 4. -3xy? + 5x²y² = 2x² %3D

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: