Computer Science · Data Sheet

Differential Calculus Cheat Sheet

Symbol	Constant	Value	Unit
d(cu)/dx	Constant multiple rule	d(cu)/dx=c du/dx	formula
d(u+v)/dx	Sum rule	d(u+v)/dx=du/dx+dv/dx	formula
d(uv)/dx	Product rule	d(uv)/dx=u dv/dx+v du/dx	formula
d(u^n)/dx	Power rule	d(u^n)/dx=n u^(n-1) du/dx	formula
d(u/v)/dx	Quotient rule	d(u/v)/dx=(v du/dx-u dv/dx)/v^2	formula
d(exp(cu))/dx	Exponential derivative	d(exp(cu))/dx=c exp(cu) du/dx	formula
d(ln u)/dx	Log derivative	d(ln u)/dx=(1/u)du/dx	formula
d(sin u)/dx	Sine derivative	d(sin u)/dx=cos(u)du/dx	formula
d(cos u)/dx	Cosine derivative	d(cos u)/dx=-sin(u)du/dx	formula
d(tan u)/dx	Tangent derivative	d(tan u)/dx=sec(u)^2 du/dx	formula
d(arcsin u)/dx	Arcsine derivative	d(arcsin u)/dx=du/dx/sqrt(1-u^2)	formula
d(arctan u)/dx	Arctangent derivative	d(arctan u)/dx=du/dx/(1+u^2)	formula
d(sinh u)/dx	Sinh derivative	d(sinh u)/dx=cosh(u)du/dx	formula
d(cosh u)/dx	Cosh derivative	d(cosh u)/dx=sinh(u)du/dx	formula
d(tanh u)/dx	Tanh derivative	d(tanh u)/dx=sech(u)^2 du/dx	formula

About this calculator

A searchable formula reference transcribed and normalized from the supplied Theoretical Computer Science Cheat Sheet.

Differential Calculus formula reference

This searchable reference organizes formulas from the supplied Theoretical Computer Science Cheat Sheet into web-friendly notation. Use the search box to find a formula by name or symbol, then review its assumptions before applying it.

Some identities use conventional mathematical notation such as summation limits, factorials, congruences, expectations and asymptotic bounds. These entries are reference material and should be interpreted within their stated domains.