Maths

Methods of a differentiation- 3

Symbols used for derivative

dy/dx or f ‘(x) or D(y) or  y’ or y1       First Order Derivative

d2y/dx2  or f ”(x) or D2(y) or  y” or  y2   Second Order Derivative

Derivative of some standard Functions

  • d(xn)/dx =nxn-1   n ∈ R; x>0     
  • d(ax)/dx =aln a    a>0
  • d(ex)/dx =ex
  • d(ln x)/dx = 1/x

Trigonometric Functions

  • d(sin x)/dx = cos x
  • d(cos x)/dx = -sin x
  • d(sec x)/dx = sec x tan x
  • d(cosec x)/dx = -cot x cosec x
  • d(tan x)/dx = sec2 x
  • d(cot x)/dx = cosec2 x

Inverse Trigonometric Functions

  • d(sin-1x)/dx = 1/(1-x2)1/2        -1<  x <1  
  • d(cos-1x)/dx = -1/(1-x2)1/2      -1<  x <1  
  • d(cot-1x)/dx = -1/(1+x2)             x∈ R
  • d(tan-1x)/dx = 1/(1+x2)              x∈ R
  • d(sec-1x)/dx = 1/|x|(x2-1)1/2     |x|>1
  • d(cosec-1x)/dx = -1/|x|(x2-1)1/2   |x|>1

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