Question

compute the derivative

y=e^xlnx and y=(lnx+e^x)5

Answer 1

1.\[y=e^xlnx\]

2.\[y=(lnx+e^x)^5 \]

Answer 2

1º
use derivative of the product rule: (uv)' = u'v+uv'
let u=e^x and v = ln x
so (e^xlnx)' =(e^x)'lnx+e^x(lnx)'=e^xlnx+e^x/x
2º
use chain rule for derivative:
[(lnx+e^x)^5]'=5(lnx+e^x)^4*(1/x +e^x)