differentiation of expotwntial functions

Question

Find the derivative of the function.
f(u) = (u^7)(e^-u)

Answer 1

f(u) = u⁷e^-u

 

 

Use the product rule: If f(u) = g(u)h(u), then df/du = dg/du h + g dh/du.

 

 

Then, du⁷/du e^-u + u⁷ de^-u/du = (7u⁶) e^-u + u⁷(-e^-u) = 7u⁶e^-u - u⁷e^-u = u⁶e^-u(7 - u)

Answer 2

f(u) = u7e-u

 

Apply the Product Rule:

 

df(u)/du = 7u⁶e^-u + u⁷(-e^-u-1)

 

     = (u⁶/e^u)(7 - u/e)