How do I find the differentiate f(x)=xsin(πx)

Answer 1

f(x) = xsin(pix)

= 1st term times derivative of the 2nd term + the 2nd term times derivative of the 1st term

= x(sin(pix)' + sin(pix)(1)

y' = x(picospix) + sinpix

y' = pixcospix + sinpix

Answer 2

f'(x) = sin(πx) + πxcos(πx) (Product and chane rules)