Formula for Differentiation | Mathematics 2

Formula for Differentiation আজকের ক্লাসের আলোচনার বিষয়। “Formula for Differentiation” ক্লাসটি “গণিত- ২ [ Mathematics – 2 ]” এর ৭তম অধ্যায় [ Chapter 7 ] এর অংশ। এই ক্লাসটি “অটোমোবাইল টেকনোলজি [ Automobile Technology ]” কোর্সের [Course] যা “২য় সেমিস্টার [ 2nd Semester ] এর “গণিত- ২ [ Mathematics – 2 ]” এ পড়ানো হয়।

 

Formula for Differentiation

Differentiation Formulas List

In all the formulas below, f’ and g’ represents the following:

  • (())=′()
  • (())=′()

 

 

Both f and g are the functions of x and are differentiated with respect to x. We can also represent dy/dx = Dx y. Some of the general differentiation formulas are;

  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:
    ()=′–′2

Differentiation Formulas for Trigonometric Functions

Trigonometry is the concept of the relationship between angles and sides of triangles. Here, we have 6 main ratios, such as, sine, cosine, tangent, cotangent, secant and cosecant. You must have learned about basic trigonometric formulas based on these ratios. Now let us see the formulas for derivatives of trigonometric functions and hyperbolic functions.

  1. ( )=
  2. ( )=–
  3. ( )=2
  4. ( =−2
  5. ( )=
  6. ( )=−
  7. (ℎ )=ℎ
  8. (ℎ )=ℎ
  9. (ℎ )=ℎ2
  10. (ℎ )=−ℎ2
  11. (ℎ )=−ℎ  ℎ
  12. (ℎ )=−ℎ  ℎ

Differentiation Formulas for Inverse Trigonometric Functions

Inverse trigonometry functions are the inverse of trigonometric ratios. Let us see the formulas for derivatives of inverse trigonometric functions.

  1. (−1 )=11–2
  2. (−1 )=−11–2
  3. (−1 )=11+2
  4. (−1 )=−11+2
  5. (−1 )=1||2–1
  6. (−1 )=−1||2–1

 

formula for differentiation

 

Other Differentiation Formulas

  1. ()=
  2. ()=
  3. ( )=1( )
  4. ( )=1/
  5. Chain Rule:
    =×=××

 

Formula for Differentiation – Details :

 

 

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