Question

How do you find the derivative of `y=e^x*lnx`?

Answer 1

`dy/dx=e^x(lnx+1/x)`

Explanation:

`"differentiate using the "color(blue)"product rule"`

`"Given " y=g(x)h(x)" then"`

`dy/dx=g(x)h'(x)+h(x)g'(x)larr" product rule"`

`"here " g(x)=e^xrArrg'(x)=e^x`

`h(x)=lnxrArrh'(x)=1/x`

`rArrdy/dx=e^x. 1/x+lnx.e^x`

`color(white)(rArrdy/dx)=e^x(lnx+1/x)`