### INTRODUCTION

Calculus involves topics like limits, differentiation and integration that studies about the continuous changes between values that are related by a function. It helps in creating mathematical models to arrive at an optimal solution.

Let us study about differentiation and its specific rules

**Differentiation:**

Differentiation allows us to find the rate of change of a function or a quantity. For example, the differentiation of y with respect to x,written as helps to compute the variation of y with respect to x, which is nothing but the gradient of the y-x curve.

**Rules of differentiation:**

**Calculas:**

**2.Sum and difference rule:**

**3.Product rule:**

**4.Calculas 4:**

**4.Chain rule:** Consider the function F(x) to be the composite function defined by F(x) = f(g(x)) then

**Integration:**

It is the reverse process of differentiation in which a function can be found out from its derivative.It is denoted by the symbol “ ∫ “. Integration can be used to find areas, volumes, central points and many useful things.

**Rules of integration:**

**1.Multiplication by constant:**

**∫c f(x) dx = c∫ f(x) dx**

**2.Sum and difference rule:**

**∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx**

**∫(f(x) - g(x)) dx = ∫f(x) dx - ∫g(x) dx**

**3.Integration by parts:**

**∫ udv = uv - ∫ vdu**

Choose u in this order :** ILATE**

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**4.Substitution rule:**

If the integral is of the form ∫ f(g(x) g’(x) dx we use this method whose value is given by

**∫ f(g(x) g’(x) dx = F(g(x)) + c**

**Where F(x) = ∫f(x) dx**