Differentiation Formula

Differentiation Formula

Differentiation is an important topic for higher class mathematics and science related subjects.  Here I have shared most of the common used formula for differentiation. Students can refer these to solve their mathematical problems. I have suplied a PDF version of this page.
You can download it by clicking on highlighted Download PDF.

Topics on this page:

  • basic differentiation formula,
  •  differentiation formula for trigonometric function, 
  • differentiation formula for inverse trigonometric functions and
  • differentiation formula for power and logarithmic function.

 Some basic differentiation Formula

These are basic rule fore defferention.
  1. \(\frac{d}{dx}x^n=nx^{n-1}\)
  2. \(\frac{d}{dx}x=1\)
  3. \(\frac{d}{dx}√x=\frac{1}{2√x}\)
  4. \(\frac{d}{dx}a=0\)

Differentiation Formula ,whare u and v are function of x

Here we have considered u and v as function of x . 

  1. \(\frac{d}{dx}au=a\frac{d}{dx}u\)
  2. \(\frac{d}{dx}(u+v)=\frac{d}{dx}u+\frac{d}{dx}v\)
  3. \(\frac{d}{dx}(u-v)=\frac{d}{dx}u-\frac{d}{dx}v\)
  4. \(\frac{d}{dx}(uv)=u\frac{d}{dx}v+v\frac{d}{dx}u\)
  5. \(\frac{d}{dx}(\frac{u}{v})=\frac{v\frac{d}{dx}u-u\frac{d}{dx}v}{v^2}\)

Differentiation Formula for trigonometric function

  1. \(\frac{d}{dx}sinx=cosx\)
  2. \(\frac{d}{dx}cosx=-sinx\)
  3. \(\frac{d}{dx}tanx=sec^2x\)
  4. \(\frac{d}{dx}cotx=-cosec^2x\)
  5. \(\frac{d}{dx}secx=secx tanx \)
  6. \(\frac{d}{dx} cosecx=-cosecx cotx \)

Differentiation Formula for inverse trigonometric function

  1.  \(\frac{d}{dx}sin^{-1}x=\frac{1}{\sqrt{1-x^2}}\)
  2. \(\frac{d}{dx}cos^{-1}x=-\frac{1}{\sqrt{1-x^2}}\)
  3. \(\frac{d}{dx}tan^{-1}x=\frac{1}{1+x^2}\)
  4. \(\frac{d}{dx}cot^{-1}x=-\frac{1}{1+x^2}\)
  5. \(\frac{d}{dx}sec^{-1}x=\frac{1}{|x|\sqrt{x^2-1}}\)
  6. \(\frac{d}{dx}cosec^{-1}x=-\frac{1}{|x|\sqrt{x^2-1}}\)

Differentiation Formula for power and logarithmic function

  1. \(\frac{d}{dx}a^x=a^x lna\)
  2. \(\frac{d}{dx}e^x=e^x\)
  3. \(\frac{d}{dx}e^{mx}=me^mx\)
  4. \(\frac{d}{dx}lnx=\frac{1}{x};(x>0)\)
  5. \(\frac{d}{dx}log_ax=\frac{1}{x lna}=\frac{1}{x}log_a e\)
                Download PDF

Note: Viewers,if you face any error or missing, please comment below.

إرسال تعليق (0)
أحدث أقدم