Find d 2 y/dx 2 if y = x tan x.

We can use the product rule to solve the derivative of y = x tan x: dy/dx = x(secx)^2 + tan x Now we can substitute y into the derivative of d 2 y/dx 2 : d 2 y/dx 2 = 2(secx)^2 + x(secx)^2 + tanx Simplifying it gives us: 2secx^2 + xsecx^2 + tanx(secx)^2, which is equivalent to choice C.

Find d 2 y/dx 2 if y = x tan x.

We can use the product rule to solve the derivative of y = x tan x: dy/dx = x(secx)^2 + tan x Now we can substitute y into the derivative of d 2 y/dx 2 : d 2 y/dx 2 = 2(secx)^2 + x(secx)^2 + tanx Simplifying it gives us: 2secx^2 + xsecx^2 + tanx(secx)^2, which is equivalent to choice C.