Thursday, February 19, 2009

Calculus Formulas: Finding Derivatives

Basic Formulas of Derivatives

For any two differentiable functions f(x) and g(x):

  1. f(x)=c (c is a constant), then f'(x)=0
  2. g(x)=cf(x) (c is a constant), then g'(x)=c·f'(x)
  3. f(x)=xn (n is a rational number), then f'(x)=nxn-1
  4. y=f(x)±g(x), then y'=f'(x)±g'(x)
  5. y=f(x)·g(x) then, y'=f'(x)·g(x)+f(x)·g'(x)
  6. y=f(x)/g(x) (g(x)≠0) then, y'=(f'(x)g(x)-f(x)g'(x))/g2(x)

Derivatives of Various Functions

  1. y=ex then, y'=ex
  2. y=ax then, y'=ax·ln(a)
  3. y=ln(x) then, y'=1/x
  4. y=logax then, y'=1/(x·ln(a))
  5. y=sin(x) then, y'=cos(x)
  6. y=cos(x) then, y'=-sin(x)
  7. y=tan(x) then, y'=1/cos2(x)
  8. y=arctan(x) then, y'=1/(x2+1)
  9. y=arcsin(x) then, y'=(1-x2)-0.5

Derivative of Composite Functions

  1. y=f(u), u=g(x) then, dy/dx=dy/du · du/dx
  2. y=f(ax+b) then, y'=af'(ax+b)
  3. y=fn(x) then, y'=n·fn-1(x)·f'(x)

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