Rayleigh density is given (“e" is a real constant): Here exp represents the exponential function: e^ f(x) = [x / c² ] exp( -x²/ ( 2 c² ) ) u(x) where u(x) is unit-step function .

Q: The current, I, in an RLC circuit is given by the equation: R d’I dI + 2a +®;I = 0 (1) dt? dt V C…

A: Given that, It=e-αtsinωt is the solution of the given differential equation.where,α=R2L and…

Q: part ii, thank you very much.

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Q: Consider the function f(x)= (3x-e^x)/2   a) Rewrite f(x) so that you can just use the power rule and…

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Q: Q1/ Find dy/dx for the followings functions: 3 x(x+1)(x-2) 1) y = use logarithmic differentiation…

A: From the given problem:   y=xx+1x-2x2+12x+33   Now we can simply write as:   y=xx+1x-2x2+12x+313…

Q: Find f′(x).   ​f(x)= ln x/27+x

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Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

Q: Find the derivative of f(x) = e* (3x' - 4) %3D

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Q: Determine t′(x) if t(x)=(arctan(x))^13

A: Given tx=arctanx13.We need to find t'x.Formula to be used:ddxxn=nxn-1ddxarctanx=11+x2

Q: Find dy/dx if f(x) = csc (x³ + x + 1)

A: Derivative of the function

Q: Find f′(x). f(x)=5x4 ln x

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Q: Determine h′(x) if h(x)=(cot−1(x))5.

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Q: Find the derivative of f(x) = e2" (3a? - x)

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Q: Show that the derivative of ! log (9-1)(g-1)u²+2u–1 u e [0, 1], q 2 3 > 0 for u > 1+(q-1)(2–u)u

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Q: Find f'(z) of f(z) = Log(z2i).

A: Given complex function is  f(z)=log(z2i)

Q: Find f′(x) if f(x) = lnx / x2

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Q: Find f. (x + 1) f'(x) = (1) = 3 %3D f(x) =

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Q: Let f(x) = 5 · In(e² · x). Let g =f-1. Find g(10), f'(x) and g'(10)

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Q: Let f(v) be the gas consumption in liters/km of a car traveling at velocity v km/hr. In addition,…

A: f(v) be the gas consumption of a car travelling at velocity v km/hr.f(60)=0.05f'(60)=0.0005

Q: Let g(x) = f(t) dt, where f is the function whose graph is sho %3D yA f 1 1 6. 6. 3.

A: you can say that the given graph is the graph of g'(x). so directly from graph g'(3) = 3