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: 3. Determine the derivative of the function with respect to x. (Arrange your answer from highest…

A: We are given: y=(x2+1)(x3-x2)⇒y=x5-x4+x3-x2 We need to find its derivative. This can be done as…

Q: У y = |1 - х - 1+х

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Q: A particle performs a movement on the same line from the origin. The equation that determines your…

A: Topic : differentiation

Q: Find the derivative of the following function. 3 f(w) = 9w° + 6w + 7w

A: Given,          f(w)=9w5 + 6w3 +7w

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

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Q: Evaluate the first derivative of the function below at (1, -2). 3x4y² - 7xy³ = 4 - 8y

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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: (x² – y²)² – 4ay³ = yCosx + xCosy = 1

A: We have to find the derivative of the above functions .

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

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Q: Find the third derivative of the following function: f (x) = 10x³ (x + 20) 240x + 1200 dæ3 240x +…

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Q: 2t –8 Find the derivative of with respect to t. 4t+8 3t а. (4t+8)² 3t b. (4t+8)? 3 C. (t+2)? 3. d.…

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Q: 1. Find the derivatives of the following function (a) y=4²+2

A: Given function y=4x2x-3xx+2xx             =4x-3+2x Differentiate y with respect to x dydx=ddx4x-3+2x…

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: