We use the PRODUCT RULE when the function that we need to differentiate is actually two functions multiplied together: If y=uvy=uv (meaning uu multiplied by vv) then: dydx=udvdx+vdudxdydx=udvdx+vdudx...

Differentiate:     y=5x9e4xy=5x9e4x

First identify the two functions  uu  and  vv:

u=u=                    v=v=

Now differentiate each one:

dudx=dudx=                    dvdx=dvdx=

Substitute each component into the formula in the correct place:

dydx=dydx=××++××

Finally tidy this up to give your final answer:

dydx=dydx=