Skip to main content
Logo image

APEX Calculus

Section B.1 Differentiation Formulas

List B.1.1. Derivative Rules
  1. ddx(cx)=c
  2. ddx(u±v)=u±v
  3. ddx(uv)=uv+uv
  4. ddx(uv)=vuuvv2
  5. ddx(u(v))=u(v)v
  6. ddx(c)=0
  7. ddx(x)=1
List B.1.2. Derivatives of Elementary Functions
  1. ddx(xn)=nxn1
  2. ddx(ex)=ex
  3. ddx(ax)=lnaax
  4. ddx(lnx)=1x
  5. ddx(logax)=1lna1x
  6. ddx(sin(x))=cos(x)
  7. ddx(cos(x))=sin(x)
  8. ddx(csc(x))=csc(x)cot(x)
  9. ddx(sec(x))=sec(x)tan(x)
  10. ddx(tan(x))=sec2(x)
  11. ddx(cot(x))=csc2(x)
  12. ddx(cosh=(x))=sinh(x)
  13. ddx(sinh(x))=cosh(x)
  14. ddx(sech(x))=sech(x)tanh(x)
  15. ddx(tanh(x))=sech2(x)
  16. ddx(csch(x))=csch(x)coth(x)
  17. ddx(coth(x))=csch2(x)
List B.1.3. Derivatives of Inverse Functions
  1. ddx(sin1(x))=11x2
  2. ddx(cos1(x))=11x2
  3. ddx(csc1(x))=1|x|x21
  4. ddx(sec1(x))=1|x|x21
  5. ddx(tan1(x))=11+x2
  6. ddx(cot1(x))=11+x2
  7. ddx(cosh1(x))=1x21
  8. ddx(sinh1(x))=1x2+1
  9. ddx(sech1(x))=1x1x2
  10. ddx(csch1(x))=1|x|1+x2
  11. ddx(tanh1(x))=11x2
  12. ddx(coth1(x))=11x2
You have attempted 1 of 1 activities on this page.