11+ Derivative Of X Power 1/2 Images. The reason is that it is a simple rule to remember and it applies to all different kinds of functions. Learn how to find the derivative of any number raised to the power of x.

Proof of derivative of y = a^x - YouTube from i.ytimg.com

Multiply by power then reduce power by 1. The derivation calculation (first order derivative ) is based mainly on a list of usual derivatives , already calculated and known (see below). Since b, definition a constant value never changes, the derivative of a constant will always be 0.

Interactive graphs/plots help visualize and better.

Here is the power rule with some sample values. Wolfram|alpha is a great calculator for first, second and third derivatives; The last two terms can be differentiated using the basic rules. In the given example, function of $x^x$, we can substitute for $x$ in power as $y$.