Find y as a function of t if 4y" +12y +9y = 0, y(0) = 6, y(0) = 6. 42 y(t) = 6 cos(-¹)+sin(-)

Q: Differentiate the following function COS T 1 (a) sec(x) tan(x) (b) (c) sin (4x° + cos(x))

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Q: (5) If y = sin(3x) the find y"

A: We have given trigonometric equation  y=sin3x y'=dydx y'=ddxsin3x y'=cos3x·ddx3x y'=3cos3x…

Q: 3. y cos (sin'x)

A: For the given  y = Cos4(sin3x) dy/dx is calculated as shown below

Q: Let g(z) = 6e²+ 9 cos z Determine the derivative of g. g'(z) = 6e²-9 sin(z) ✓ Determine the…

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Q: Consider the function Suppose that g(6) = ƒ' (6) = f(x) = (1 + sin(x)) (*) -9 and g'(6) - 4.

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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 f(x) 39 27 O 1 4√3 O-√6 9 3√3 .-1 (²). Then the second derivative at x = -1,f"(-1), equals = COS

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Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: Compute the derivative: tan-'(ax) (bx) (a) y = sin='(x²) (b) y = (tan-1 r)³ (c) y = sin

A: (a)   Differentiate the given equation with respect to x, dydx=ddxsin-1x2=11-x22ddxx2=2x1-x4

Q: Find the y'(0) when y = cos (sec²(2x))

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Q: Find f. f(x) = f"(x) = 5ex - 7 sin(x), f(0) = 3, ( 77 ) = 0 EN 2

A: Given :f''x=5ex-7sinx

Q: 6.) Find the derivative of the following functions a.) f(x)=- 7-3х |t +1 b.) f(x)=. -1 c.) f(x)= ean…

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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…