Derivatives of Sine and Cosince Functions

Question

y=xsin3x

Answer 1

Given that y = x sin3x

Differenciating on both sides we get,

     dy/dx = d/dx(x sin 3x)

This is in uv form => d(uv)/dx =uv' + vu'

              = (x) d/dx(sin3x) + sin3xd/dx(x) + c

              = (x)(3cos3x) + sin3x(1) + c           [ Since dx/dx = 1 and (d/dx)(sin(ax)) = acos(ax) ]

              = 3x cos3x + sin3x + c

Therefore d/dx(x sin 3x) = 3x cos3x + sin3x + c.