Question

What function do you know from calculus is such that its first derivative is a constant multiple k of itself

Answer 1

Answer:

Exponential function if the form $e^{Kx}$ is the constant multiple K of itself if.

$y'=\frac{dy}{dx}=cKe^{Kx} \\y'=Ky$

Step-by-step explanation:

The exponential function of the form $e^x$ 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 $e^{Kx}$ is the constant multiple K of itself if we take the dervative.

Mathmatical Prove:

Consider the general equation

let $y=ce^{Kx}$

Where:

K is a constant

c is the cofficient(could be any number)

Now:

Taking derivative of above equation w.r.t x:

$y'=\frac{dy}{dx}=cKe^{Kx} \\y'=Ky$

Hence proved exponential function is a constant multiple K of it self.