What is the derivative of

Question

y=t(sin(lnt) + cos(lnt) )? 

Answer 1

y = t (sin (ln t) + cos (ln t)) 

Apply multiplication rule of derivative  uv = uv’ + vu’ .

y' = t[ cos(ln t)*(1/t) - sin(ln t)*(1/t) ] + (sin (ln t) + cos (ln t))                       

y' = t(1/t)[ cos(ln t) - sin(ln t) ] + (sin (ln t) + cos (ln t))

y' = cos(ln t) - sin(ln t) +  (sin (ln t) + cos (ln t)) 

y' = 2cos(ln t)