(d) x²y" — 7xy' + 16y = 0, - ..!! 16a Y₁ = x¹; (102)

Q: Find the derivative of the following functions: (a) f(x) = 6x² — 83 - 12/20 2-4√x (b) y = 6 cos(3x)…

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Q: Find fif f'(x) = 2 + cos(x), f(0) = −5, ƒ(π/2) = −8.

A: Given, the information f''(x)=2+cosx, f(0)=-5, fπ2=-8. We have to find f.

Q: 3. Find the derivative. sh (a)l= - पक) (a) f(x) = x2 cos x +x tan r (b) h(x) = e" (x² + 4x) %3D t2…

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Q: Suppose h = fog. Find h'(0) given that f(0) = 8, f'(2) = -7, g(0) = 2, and g'(0) = 3. h'(0) =

A: Given that, ,  and .The aim is to find the value of .

Q: For f(x)=In(cos(x)), what is

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Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: Find f'(x) and f'(c). Function f'(x)= f'(c) = f(x) sin x x Value of c π 3

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Q: What is g'(x) when g(x) = ln Provide your answer below: g'(x) = 3x²+6x+7 x 3 cos x

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Q: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: I need to find the derivative of the function f(x) = cos-1(ln(sin(3x+1))) but I am unsure how to…

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Q: If we are told that f'(5) = 6 evaluate h'(0) where h(1) = f(5 cos r + x² + 2x).

A: Given function h(x)=f(5cosx+x7+2x)

Q: If h(a) = h(b), then what is the value of ·b [ g(h(x))h' (x)dx

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Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: 3. Use logarithmic differentiation to find y'; and simplify the result to a "single fraction". x2…

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Q: If g(x) = 2 cos¹ (4x), find g'(x). g'(x) =

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Q: k(x) = 2 6e-4x tan(x) find the equation for k'(x).

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Q: If f(x) = cos(In(x5)), find f'(1). f'(1) =

A: Explaination of the answer is as follows