Answer:
Exponential function if the form [tex]e^{Kx}[/tex] is the constant multiple K of itself if.
[tex]y'=\frac{dy}{dx}=cKe^{Kx} \\y'=Ky[/tex]
Step-by-step explanation:
The exponential function of the form [tex]e^x[/tex] is the function which is the derivative of itself.
Where:
x is independent variable
Now if we talk about constant then again exponential function if the form [tex]e^{Kx}[/tex] is the constant multiple K of itself if we take the dervative.
Mathmatical Prove:
Consider the general equation
let [tex]y=ce^{Kx}[/tex]
Where:
K is a constant
c is the cofficient(could be any number)
Now:
Taking derivative of above equation w.r.t x:
[tex]y'=\frac{dy}{dx}=cKe^{Kx} \\y'=Ky[/tex]
Hence proved exponential function is a constant multiple K of it self.
