What is the derivative of e^(x^5 cosx)

What is the derivative of e^(x^5 cosx)?

How I'm seeing it, it should be e^(x^5*cosx)*(5x^4 cosx)*(-sinx) but that's apparently wrong.

d/dx [ e^ (x^5 cos x) ] = e^(x^5 cos x) d/dx (x^5 cos x)
= e^(x^5 cos x) ( 5x^4 cos x -x^5 sinx)

Note:
you apply the product rule to differentiate x^5 cos x