Answer: The derivative of the function [tex]y=e^{5x}[/tex] is [tex]5e^{5x}[/tex] .
Step-by-step explanation:
We know that the derivative of [tex]e^{ax}[/tex] with respect to x is given by :
[tex]\dfrac{d}{dx}(e^{ax})= a e^{x}[/tex] (1)
The given function is [tex]y=e^{5x}[/tex]
Differential both sides with respect to x , we get
[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(e^{5x})[/tex]
[tex]\Rightarrow\ \dfrac{dy}{dx}=5e^{5x}[/tex] ( Using (1))
Therefore , the derivative of the function [tex]y=e^{5x}[/tex] is [tex]5e^{5x}[/tex] .
