Using the definition of  the derivative, the derivatives of some essential core functions can be visualized with mapping diagrams:

These core functions can then be used along with the calculus of derivatives to differentiate all elementary functions.

CCD.DP: The derivatives of the power functions: integer powers.

CCD.DS: The derivatives of the sine and cosine functions.

CCD.DE: The derivative of the natural exponential function.

CCD.DL: The derivative of the natural logarithm function.

Dynamic visualization of the definitions of the derivative: