Find y'' if y equals 6x sinx?

Answer 1

That means you must take the derivative of the derivative. In this case, you must use the product rule.

y = 6x sin x

y'= 6[x (sin x)' + (x)' sin x]

= 6[x cos x + sin x]

y'' = 6[x (cos x)' + (x)' cos x + cos x]

= 6[x (-sin x) + cos x + cos x]

= 6[-x sin x + 2 cos x]