Rules of Calculus

Power Rule:

Simple: $x^n$ → $n{x}^{n-1}$

Sum Rule:

$\frac{d}{dx}(g(x)+h(x))=\frac{dg}{dx}+\frac{dh}{dx}$

Think of the tiny changes in both of the individual functions

Product Rule:

$f(x)=g(x)h(x)$
Then $\frac{df}{dx}=\frac{dg}{dx}h+\frac{dh}{dx}g$
Think of the rectangle.

Chain Rule

If $f(x)=g(h(x))$
Then $\frac{df}{dx}=\frac{dg(h)}{h}.\frac{dh}{dx}$
Think of this as 3 separate number lines. The change in $h$ ($dh$) depends on the change in $x$ ($dx$). The change in $g$ ($dg$) depends on $dh$. If we differentiate starting from the outermost layer, everything falls into place.

Derivative Rules / Rules of Derivation / Derivatives: