What function do you know from calculus is such that its first derivative is itself? its first derivative is a constant multiple of itself? write each answer in the form of a first-order differential equation with a solution.

First Part:

exponential function is the one whose first order derivative is the function itself.

Second Part:

Third Part:

Step-by-step explanation:

First Part:

In calculus exponential function is the one whose first order derivative is the function itself.

Where:

t is independent variable.

Derivative is represented as:

Where:

c is any number.

Second Part:

Consider the constant A.

The function will become:

Third Part:

Derivative is represented as:

Where:

c is any number.

i would say the third one.

step-by-step explanation: liner would mean in a line and the only one that doesn't look like it's even thinking about forming a line would be the third one