**Differentiation formulas pdf class 12:** Differentiation is an important topic of class 12th Mathematics. Differentiation is an important concept in Calculus, on the other hand integration also involves the usage of Differentiation formulas and concepts to solve the integration questions.

Differentiation is used to find the derivative of a defined function, it is also used in calculating instantaneous rate of change or variation in functions which is most commonly used in Physics and Chemistry.

## Differentiation formulas pdf

Contents

Suppose there are two variables X and Y then the rate of change of X with respect to Y is given by d(x)/dy. It is also denoted in the form of f'(x) where the apostrophe sign denotes differentiation. Single apostrophe sign denotes general derivative, which means it is single-order derivative. While there are higher order derivatives in class 12 which are denoted by double or triple apostrophe signs in which double apostrophe denotes second order derivative and so on.

Second degree or order derivative means a function undergoes differentiation two times.

The Second order derivative is also denoted in the form of d2(x)/dy, where X is a function.

It is pronounced as “Differentiation of X with respect to Y”

In class 12th there are only 1st and 2nd order derivatives as per NCERT syllabus but many schools give efforts to 3rd order derivatives also.

**Rules of Differentiation **

There are four rules of Differentiation which are given below:-

- Sum and difference Rule
- Product Rule
- Quotient Rule
- Chain Rule

**Sum and Difference Rule**

If the function is in the form f(x)=u(x)±v(x) the it’s differentiation is given by

f'(x)=u'(x)±v'(x)

It is called Sum or difference rule.

**Product Rule**

If there are two sub functions in any function then product rule is used which is given by

If f(x)=u(x)×v(x) then its differentiation is given by

f'(x)=u(x)×v'(x)+v(x)×u'(x)

**Quotient Rule**

Quotient Rule is used when functions are in the fractional form where denominator is not equal to one.

If f(x)=u(x)/v(x) then differentiation is given by

f'(x)=[u'(x)×v(x)-v'(x)×u(x)]/[v(x)]²

**Chain Rule**

Chain rule is used when there is series or pattern in function is observed.

f'(x)/f'(y) is given by [d(x)/du] × d(u)×d(y)

There are some formulas also in differentiation which are given below

Function or d(x)/d(y) | Derivative |

Sinx | Cosx |

Cosx | -Sinx |

Tanx | Sec²x |

Cotx | -Cosec²x |

Secx | Secxtanx |

Cosecx | -Cosecxcotx |

Sin^{–}¹x |
1/(1-x²)1/2 |

Cos^{-1}x |
-1/(1-x²)1/2 |

Tan^{-1}x |
1/(1+x²) |

Cot^{-1}x |
-1/(1+x²) |

Sec^{-1}x |
1/(|x|)(x²-1)1/2 |

Cosec^{-1}x |
-1/(|x|)(x²-1)1/2 |

These are some important differentiation formulae used in class 12th.

**Applications of Differentiation **

There are numerous applications of Differentiation which are given below.

- Finding Rate of Change of a Quantity
- Finding the Approximation Value
- Finding the equation of a Tangent and Normal To a Curve
- Finding Maxima and Minima, and Point of Inflection
- Determining Increasing and Decreasing Functions
- Especially in Science, study related to nuclear decay, chemical engineering involves the awesome usage of Differentiation.

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