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**Basic part **

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*Mathematical tools everyone should know*

*Mathematical tools everyone should know*

**Graph:**It is the fictional representations of variation of one quantity with respect to another quantity. Shape of graph depends on the relation between two variables.

*standard*equation came from graph, its prove discuss later in math and link will be updated here.

y = mx where 'm' is slope of straight line.

from the above fig.1., m = tanθ = [(y2 -y1)/(x2-x1)]

fig.1. |

tanθ = (Δy/Δx)

Differentiation:

*change in a function w.r.t. another function.*

*If we draw a graph for function,the derivative at a certain point corresponds to the 'slope' or 'gradient' of the function at that point as in fig.2.*

fig.2. |

Consider a continuous curve y=f(x) and P be a point on this curve.If tangent to the curve at P makes an angle with the x-axis then at point P

dy/dx= tanθ = m

Case 1:If dy/dx

then the tangent makes an acute angle with x-axis as in fig.3.

fig.3. |

Case 2:If dy/dx

then the tangent makes an obtuse angle with x-axis as in fig.4.

fig.4. |

Case 3:If dy/dx

then the tangent is parallel to x-axis as in fig.5.

fig.5. |

**Rules for differentiation:**

**1(a).**Derivative of a constant function is zero.

i.e. dy/dx(k)=0

**(b).**Let c is a constant and f(x) is a differentiable function then

i.e.

**2.**If two functions are given then rename

**(a).**

**(b).**

*(product rule)*

**(c).**

provided v≠0

*(quotient rule)*

**3.**Derivative of a function of function

*(Chain rule)*

If y is differentiable function of 'u and u' is differentiable function of 'x' then

**Some important results**

**Integration:**

**Anti derivative**

**or**Inverse of differentiation.

Standard integral formulae:

—vvv —

Great👍

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