Find d²/dx² (sin x + cos x).

Explain why or why not Determine whether the following statements are true and give an explanation or counter example.

b. d²/dx² (sin x) = sin x.

A differential equation is an equation involving an unknown function and its derivatives. Consider the differential equation y′′(t)+y(t) = 0.

b. Show that y = B cos t satisfies the equation for any constant B.

Find y'' for the following functions.

y = x sin x

Find y'' for the following functions.

y = tan x

Find y'' for the following functions.

y = cos θ sin θ

Find y⁽⁴⁾ = d⁴y/dx⁴ if:

a. y = −2 sin x

Find y'' if:

a. y = csc x