How do you find the derivative of #f(x)=5e^x#?

All that is here is a constant, #5#, multiplied with the function #e^x#. When differentiating a function that is multiplied a constant, just differentiate the other function and then multiply that by the constant.

Dal momento che il derivato di #e^x# è altresì #e^x#, when you differentiate the function, the #e^x# remains, and it is also multiplied by the #5#, giving the derivative of, again, #5e^x#.

We can see this as:

#f'(x)=d/dx(5e^x)#

Taking the constant out:

#f'(x)=5*d/dx(e^x)#

Dal momento che il derivato di #e^x# is #e^x#:

#f'(x)=5*e^x=5e^x#