x^2 e^x sin x

Question

Find the derivation of function

x² e^x sin x

Answer 1

y = x² e^x sin x 

Let u = x², v = e^x and w = sin x 

u’ = 2x, v’ = e^x and w’ = cos x 

y’ = uvw’ + vwu’ + uwv’ 

= (x²e^x) cos x + (e^x sin x)(2x) + (x² sin x)e^x 

= x² e^x cos x + 2xe^x sin x + x² e^x sin x 

= xe^x {x cos x + 2 sin x + x sin x}