Differentiation Formulas

Differentiation formulas list has been provided here for Math students so that they can refer these to solve problems based on differential equations. This is one of the most important topics in higher class Mathematics. The general representation of the derivative is d/dx.

This formula list includes derivative for constant, trigonometric functions, polynomials, hyperbolic, logarithmic functions, exponential, inverse trigonometric functions etc. Based on these, there are a number of examples and problems present in the syllabus of class 11 and 12, for which students can easily write answers.

Differentiation  Formulas

 

In all the formulas below, f’ means \( \frac{d(f(x))}{dx} = f'(x)\) and g’ means \(\frac{d(g(x))}{dx}\) = \(g'(x)\) . Both f and are the functions of x and differentiated with respect to x. We can also represent dy/dx = Dx y.

  1. Power Rule: (d/dx) (xn )nxn-1
  2. Derivative of a constant, a:  (d/dx) (a) = 0
  3. Derivative of a constant multiplied with function f: (d/dx) (a. f)af’
  4.  Sum Rule: (d/dx) (f ± g) = f’ ± g’
  5. Product Rule: (d/dx) (fg)= fg’ + gf’ 
  6. Quotient Rule:\(\frac{d}{dx}(\frac{f}{g})\) = \(\frac{gf’ – fg’}{g^2}\)
  7. \(\frac{d}{dx} (sin~ x)\) = cos x
  8. \(\frac{d}{dx} (cos~ x)\) = – sin x
  9. \(\frac{d}{dx} (tan ~x)\) = sec2 x
  10. \(\frac{d}{dx} (cot~ x)\) = -csc2 x
  11. \(\frac{d}{dx} (sec~ x)\)sec x tan x
  12. \(\frac{d}{dx} (csc ~x)\) = -csc x cot x
  13. \(\frac{d}{dx} (sinh~ x)\) = cosh x
  14. \(\frac{d}{dx} (cosh~ x)\) = sinh x
  15. \(\frac{d}{dx} (tanh ~x)\)= sech2 x
  16. \(\frac{d}{dx} (coth~ x)\) =-csch2 x
  17. \(\frac{d}{dx} (sech~ x)\) = -sech2 x  tanh x
  18. \(\frac{d}{dx} (csch~ x )\) = -csch x  coth x
  19. \(\frac{d}{dx}(sin^{-1}~ x)\) = \(\frac{1}{\sqrt{1 – x^2}}\)
  20. \(\frac{d}{dx}(cos^{-1}~ x)\) = \(-\frac{1}{\sqrt{1 – x^2}}\)
  21. \(\frac{d}{dx}(tan^{-1}~ x)\) = \(\frac{1}{1 + x^2}\)
  22. \(\frac{d}{dx}(cot^{-1}~ x)\) = \(-\frac{1}{1 + x^2}\)
  23. \(\frac{d}{dx}(sec^{-1} ~x) \)= \(\frac{1}{|x|\sqrt{x^2 – 1}}\)
  24. \(\frac{d}{dx}(csc^{-1}~x) \)= \(-\frac{1}{|x|\sqrt{x^2 – 1}}\)
  25. \(\frac{d}{dx}(a^x) \)= ax ln a
  26. \(\frac{d}{dx}(e^x) \)= ex
  27. \(\frac{d}{dx}(log_a~ x)\) = \(\frac{1}{(ln~ a)x}\)
  28. \(\frac{d}{dx}(ln~ x)\) = 1/x
  29. Chain Rule: \(\frac{dy}{dx}\) = \(\frac{dy}{du} × \frac{du}{dx}\) = \(\frac{dy}{dv} × \frac{dv}{du} × \frac{du}{dx}\)<

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Practise This Question

If α,β are the zeros of the polynomial x2px+36 and
α2+β2 = 9, then what is the value of p?