MHT-CET : Mathematics Entrance Exam

### MHT - CET : Mathematics - Derivatives Formulae Page 1

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1. Leibnitz definition of derivative

 dy dx

=

 lim dx®0

 dy dx

2. First principle for differentiation

f'(x) =

 lim h®0

 f(x + h) - f(x) h

3. Derivative of algebraic function

 d dx

(xn) = nxn-1

4. Derivative of constant

 d dx

(c) = 0

5. Derivative of trigonometric functions

 1. d dx

(sin x) = cos x

 2. d dx

(cos x) = - sin x

 3. d dx

(tan x) = sec2 x

 4. d dx

(cot x) = - cosec2x

 5. d dx

(sec x) = sec x tan x

 6. d dx

(cosec x) = - cosec x cot x

6. Derivative of y = u ± v

 dy dx

=

 du dx

±

 dv dx

7. Derivative of y = uv

 dy dx

= u

 dv dx

+

 du dx

8. Derivative of y = u/v

 dy dx

=

v

 du dx

-

 dv dx

v2

9. Derivative of product of functions

If y uvw,

 dy dx

= vw

 du dx

+ uw

 dv dx

+ uv

 dw dx

10. Chain rule

If y = f (u), u = g(v), v = h(x),

 dy dx

=

 dy du

x

 du dv

x

 dv dx

11. Derivative of inverse trigonometric functions

 1. d dx

(sin-1x)

=

 1

 2. d dx

(cos-1x)

=

 -1

 3. d dx

(tan-1x)

=

 1 1 + x2

 4. d dx

(cot-1x)

=

 - 1 1 + x2

 5. d dx

(sec-1x)

=

 1 x

 6. d dx

(cosec-1x)

=

 - 1 x

12. Derivative of exponential functions

 1. d dx

(ex) = ex

 2. d dx

(ax) = ax log a

 3. d dx

(log x) = 1/x

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