S Show that {cos(kt)} = $2+k2 using the following two facts: L{f'(t)} = sF(s) - f(0) and • L{sin(kt)} = k $2+k2

Q: Let f(x) = 9 cos(sin(z°)). %3D Then f'(x),

A: Using the chain rule of differentiation,

Q: Let f(x) = 3 cos a - 2 tan a f'(x) = r() - C f'

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Q: Let f(x) = 9 cos(cos x) f'(x) =

A: The given function is fx=-9coscosx. We know that if fx is a function then f'x if the derivative of…

Q: 25 (6x + 5)³ But Do NOT use the Quotient Rule. a) Let f(x) = = f'(x) = Find f'(x). b) Let g(x) = 6…

A: We have to find the firstd erivative of the given functions.Recall some basic formulas: ddxxn=nxn-1…

Q: Let f(x) f'(-) = 8x sin(x) + cos(x) Evaluate f'(x) at x = -T.

A: INTRODUCTION Differentiation is a fundamental concept that involves finding the rate of change of a…

Q: Let f(z) = (9 sin z + 2 cosz)tan¹z

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Q: et ƒ(x) = 3x² cos(4x). ='(x) = −12x² sin(4x) + 6x cos(4x) (2) = 17.245 "(2) = =

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Q: Let f(x) = tan (cos(2æ)) f'(x) = Preview

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Q: 1– cos(x) y = = csc(x) – cot(x) sin(x)

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Q: Let f(x) = – 7 cos(cos æ) %3| f'(x) =

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Q: Let f(x) = 6 sin ¹(x²). Then f'(x) equals 12x √1-x² 1 1- x4 6 /1-x² 12x cos−¹(x²) 12x √1 x4

A: The objective is to find the derivative of f(x).

Q: Let f(x) = 3 cos5 x. f'(x) =

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Q: Verify that 2tan (x/2)= (sin2x+1-cos2)/(sin x(1+cos x)

A: Consider the given condition that,2tan (x/2) = (sin2x+1–cos2x)/(sin x(1+cos x)) … (1)Consider the…