Poop-Loops said:
ludi_srbin said:Oh I see. I guess I shouldn't have assumed that it is a second derivative. Thanks for the help.
The equation for y=e^nx is a basic exponential function where e is the base of the natural logarithm and n is the exponent. It can also be written as y=ex^n, where x is the independent variable.
d^ny/dx^n represents the nth derivative of y with respect to x. In other words, it is a measure of the rate of change of the exponential function y=e^nx at a specific point on the curve.
To solve for d^ny/dx^n, you will need to take the nth derivative of the exponential function y=e^nx. This can be done using the chain rule, where you multiply the original function by the derivative of the exponent, n, and then take the derivative of the exponent itself. The resulting equation will be d^ny/dx^n=ne^nx.
When n=0, the equation y=e^nx simplifies to y=e^0, which equals 1. Therefore, the value of d^ny/dx^n when n=0 is 0, as the derivative of a constant is 0.
The value of n affects the slope of the graph of y=e^nx. A larger value of n results in a steeper slope and a faster rate of growth, while a smaller value of n results in a flatter slope and a slower rate of growth. Additionally, a negative value of n will cause the graph to reflect over the x-axis, while a positive value of n will not.