Could someone help me with this?

I need to write down 4 REAL LIFE examples of the following derivative rules:

TTHIS IS ONE EXAMPLE SO YOU UNDERSTAND WHAT I NEED

The constant rule says, in Lebesgue's, apostrophy ', notation, that f(x)=c has derivative f'(x)=0.

And here is the example given to this case: f(x)=32 (in physics, the gravity acceleration on earth surface in ft/sq sec) has derivative f(x)=0

(32 is an example of a constant).

Here is what i need 4 examples for:

1. the derivative of any exponential A^X with a fixed base A, with respect to the exponent is the same function multiplied by the logarith of the base: A^x LNA
2. The derivative of LOG_AX is 1/XLNA
3. Logarithmic derivative: the derivative of f(g(x))-LN(g(x)) is the quotient (d/dx g(x))/g(x)