Calculus reference
Derivative
\[f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}h.\]Product rule
\[\frac{d}{dx}(uv)=u'v+uv'.\]Chain rule
\[\frac{d}{dx}f(g(x))=f'(g(x))g'(x).\]Partial derivative
\[\frac{\partial f}{\partial x}.\]Definite integral
\[\int_a^b f(x)\,dx.\]Fundamental theorem of calculus
If \(F'(x)=f(x)\), then
\[\int_a^b f(x)\,dx=F(b)-F(a).\]Differential notation
For differentiable \(y=f(x)\), \(dy=f'(x)dx\) expresses the differential relationship used in ordinary calculus.