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: Show that tan(y) sin(y) += cot(y) + sec(y) csc(y) 1+ cos((y) 1- cos(y)

A: NOTE: Refresh your page if you can't see any equations. . use cross multiplication

Q: The y' of the given function is (1–2 sin? 4x) y

A:

Q: Verify that if y = ƒ(θ2 sin θ, then y'(θ) = ƒ'(θ) sin θ + ƒ(θ) cos θ.

A: We use the product rule

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: 5. Find the third derivative of the function : 3 (ans. : - 8y y=Vx

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Find the derivative of f(w)= sin(4w²)+cos(4w²). A) Swcos(4w°)–8wsin(4w²) B) -8wcos(4w?)+8wsin(4w²)…

A: Given function is  f(w)=sin(4w2)+cos(4w2)Derivative of f with respect to w:f'(w)=…

Q: find y' y=cos(3x)+cot(5x)

A: We have to find derivative of f(x),where f(x) is given by:

Q: find y'. (show all the steps please) cos(xy) = x-y^2

A:

Q: what is y' of y=sin-1(cos x)

A:

Q: sinx

A:

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

A:

Q: 2, " cos“(x)sin*(x)dx

A: To find : ∫0π2cos6xsin4xdx

Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: f(x) = cos3(4x-1) Differentiate the equation

A: Given that: f(x)=cos3(4x-1)

Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

A:

Q: 13. Evaluate: sin(x²) dx A) 2x cos(x2) B) 2x sin(x?) C) 2x cos 2x D)2x cos x 14. Find the derivative…

A: To find Evaluate the integral:

Q: If x*y" + xy' + (x? - y= 0 x >0 ,V1=x 2 sinx 3D0 and y =y,v. Which of the following equations…

A:

Q: Find y' and y'". y=cos(xsin3x)

A:

Q: Find y as a function of a if a?y" + 13ry' + 36y = a, %3D y(1) = -2, y'(1) = -1. y =

A: