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Derivative Table.

c′=0,c=const;

(xα)′=αxα−1,x∈R,α∈R;

(ax)′=axln⁡a,a>0,a≠1,x∈R;

(ex)′=ex;

(loga⁡x)′=1xln⁡a,x>0;

(loga⁡|x|)′=1xln⁡a,x≠0;

(ln⁡x)′=1x,x>0;

(sin⁡x)′=cos⁡x,x∈R;

(cos⁡x)′=−sin⁡xx∈R;

(tgx)′=1cos2⁡x,x≠π2(2n+1),n∈Z;

(ctgx)′=−1sin2⁡x,x≠πn,n∈Z;

(arcsin⁡x)′=11−x2,|x|<1;

(arccos⁡x)′=−11−x2,|x|<1;

(arctgx)′=11+x2,x∈R;

(arcctgx)′=−11+x2,x∈R;

(shx)′=chx,x∈R;

(chx)′=shxx∈R;

(thx)′=1ch2x,x≠π2(2n+1),n∈Z;

(cthx)′=−1sh2x,x≠πn,n∈Z;

(arshx)′=1x2+1,x∈R;

(archx)′=−1x2−1,|x|>1;

(arthx)′=11−x2,x∈R;

(arcthx)′=1x2−1,x∈R.

Tags:

Tables and Formulas

Derivative Table.

Table of Derivatives of Composite Functions.

Table of Higher Order Derivatives.

Table of Integrals

Taylor Series

Comparison of functions O(f) and o(f).