Differential question?

Question

How would you differentiate the following?

-e^(5x+3)

Answer 1

y=-e^(5x+3)

let (5x+3)=u

y=-e^u

dy/dx = -e^u (du/dx)

dy/dx = - e^(5x+3) (5)

dy/dx = -5 e^(5x+3)  

Answer 2

u substitution....

y=-e^(5x+3)  

y '  =  -5*e^(5x+3) + k

Answer 3

(-e^(5x+3) )'

=5 (-e^(5x+3))

=-5 e^(5x+3)

Answer 4

use function of a function...

g(f(x)) differentiated is f ' (x) * g ' (f(x))

so in your case, f(x) is 5x+3

and g(x) is -e^x

so the differential is...

5 * -e^(5x+3) = -5e^(5x+3)