calculus derivatives?

liz

what is the deivative of y=10x^5e^xsin x

Update:

only use product rule

gudspeling

(uvw)' = u'vw + uv'w + uvw'

y = 10(x^5)(e^x)sin(x)

u = 10x^5, u' = 50x^4

v = e^x, v' = e^x

w = sin(x), w' = cos(x)

dy/dx=50(x^4)(e^x)sin(x) +10(x^5)(e^x)sin(x) +10(x^5)(e^x)cos(x)

dy/dx = 10(x^4)(e^x)[5sin(x) + x.sin(x) + x.cos(x)]

programhelp

product rule with the chain rule

mohanrao-d

y = 10(x^5) e^(xsinx)

let u = x^5 : du = 5x^4

v = e^(x sinx) : dv = e^(x sinx)*(x cosx + sinx )

d(uv) = udv + vdu

d[10(x^5) e^(xsinx)] =

10 x^5*(x cosx + sinx)*e^(x sinx) + 50 x^4* e^(x sinx)