Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t). Use prime notation for derivatives and write r and a', etc., instead of x (t), x'(t), or 4

Q: Find f. f ''(θ) = sin(θ) + cos(θ),    f(0) = 5,    f '(0) = 1

A: given, f ''(θ) = sin(θ) + cos(θ),    f(0) = 5,    f '(0) = 1 to find f.

Q: g(x) = 4ecoN " sin x, (0, ] COS

A: Given data:   The given function is: g(x)=4ecosxsinx The given interval is: [a,b]=[0,π].   The…

Q: Find the derivative of the following: 2x-5 y = 3x–1 O y' = 13 (3z-1) 13 (3z–1) 13 (3x+1) 13 O y' =…

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Q: Let f(x) - 6 cos 6 cos° x f '(x) =

A:

Q: Find f"(x) for the function f (x): = x cOS X

A: The given function is fx=xcosxTo find f''(x)

Q: Find f if f"(x) = 2+ cos(x), f(0) = 2, f(t/2) = -2.

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Let h(y) = 2 cos y – 7 sin y. Then h'(y) =

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Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(pi/2)=9 f(x) =

A: Solution of given question is followed by:

Q: Find F'(x), f"(x) and f'"(x) for f(x)=x$+cos(9x).

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Q: Find y" in terms of x and y. You must use implicit differentiation for this problem. 1- xy = x – Y

A: Given : 1-xy = x-y

Q: Find f if f" (x) = 2 + cos(x), f(0) = -8, f(T/2) = 8. *(x) :

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

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Q: verify tan(y)/csc(y)=1/cos(y)−1/sec(y)

A: Given data:     The given trigonometric expression is: tan(y)/csc(y) =1/cos(y) -1/sec(y).     To…