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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

dy

dx

 

2. First principle for differentiation

 

 

f'(x) =  

lim

h

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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