# Math help, not sure if the derivative of this equation is correct

Hi, in my game, I use equations to determine where something is at a certain time, I use desmos.com to visualize this.

I’m trying to create an equivalence of the derivatives at 0 of the x axis, so that the transition of the 2 equations (red runs first, then blue) are seamless.

I have 2 different time periods where the domain of my equations is 0 to 1000, both times. Unfortunately this split up the code in a way to make it easier in other ways, but harder for this question. This is not something I want to change at this time.

This is equation1:
-12.385 + 1.0028^(x+900)
Wolffram alpha says that the derivative is:
0.0346293+1.0028^x
Equation2:
149.9-.996^(x-1250)
Equation2 derivative
0.600837+.996^x

Graphed below:

It does not seem right to me that the orange (corresponding as the derivative to the red equation) is so high around 1000 on the x axis, but then the purple derivative line for the blue equation is so low around 0 of the x axis. In the game, it seems to me that the object moves a lot quicker during the start to the blue equation than toward the end of the red.

I think it has to do with derivatives and using the format of something^(x-somethingElse)

Edit: Here’s a pic closer to the 0,0

Looks like it’d be correct to subtract one from the derivative equation, not sure if that fixes other areas though

Any input is appreciated.

Both of your derivatives have + that should be × (multiplies, not additions)

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