### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Algebra of Derivatives

Let are two derivable functions of .

(i)

(ii)

(iii)

(iv)

Tangent Line of a Graph at a Point

Slope of tangent i.e.

is continous at , i.e. as i.e. as i.e exists, where is called the tangent line to the curve at .

Definition:

The tangent line of a function at the point is:

(i) The line through with slope if .

(ii) The line if .

It holds when

Indeterminant forms:

L’ Hospital’s Rule

It is pronounced “lopital”. The limit when divide one function by another is the same after we take the derivative of each function, i.e.

Note:

(i)

(ii)

(iii) , if is finite.

(iv)   is not defined, if  .

(v) iff or  and are finite.

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