Use 5-point centered difference methods to derive algebraic formulae of the first-order derivative and second-order derivative.

Q: f(x) = Arctan csc² ( 3x

A: Some derivative formulae: ddxtan-1x=11+x2ddxcscx=-cscx cotx Chain rule of derivative:…

Q: 3) у %3D 2u* + 1 x = 5u? – 5u -

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Q: Determine if the following piecewise defined function is differentiable at x = 0. 4х- 1, X20 f(x) =…

A: We will check whether the function is differntiable or not at x=0 as following.

Q: IV. Find of the following. dx 1. x-(1-2y +3y2) y-2 | 2. x = (3 + y² Xy +1)³ 3. = V1-t *ly=1 +t %3D

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Q: [3 + x? cot(x²)]-3 -3[2x cot(x²) – 2x³ sec²(x²)] [3 + x² cot(x²)]4 A -3[2x cot(x²) + 2x³ sec² (x²)]…

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Q: Which rule(s) are used to find the derivative?

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Q: 9x= (Jx+ x) (+xt) %3D

A: Given  g(x)=x+x2x3+x+2 To take derivative of g(x), we apply product rule (uv)'=u'v+v'u…

Q: Compute the derivative.

A: Here, we use product rule of differentiation to find derivative of given function.

Q: compute the derivative

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Q: Identify the derivative with complete solution.

A: The given function is fx=5sec2x+20 To find: Derivative of f(x) In the given function sec(2x) is a…

Q: R(w) = w? 8w + 20

A: Derivatives are one of  the fundamental tools of the calculus. In mathematics, derivatives are the…

Q: Determine the anti derivative of the function please

A: Here given function as fx=3ex+11-x2-2sec2x-71+x2

Q: 2. y = loga(x³ + 2x – 2) 3. y = In³(x + sin x) %3D

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Q: calculate the derivative

A: Given expression

Q: g(t) = V(1 – 3t)4 + t4

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Q: f(x)%3D (6- x²)3 — х? %3D

A: DIFFERENTIATION OR DERIVATIVE The differentiation is a process of finding the rate of change of one…

Q: a) x'+y = In xy x(t)3Darcsin VI+r' b) teR-(0} y(t)%3Darccos V1-1

A: (a) Consider the given equation. xy+yx=lnxy We have to find derivativedydxhere.…

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: