Basic Calculus

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Calculus is a branch of Mathematics which involves the study of rate of change of variables with respect to

each other and also study of their various other characteristics. Calculus forms a very important section in

Math and Basic Calculus involves calculating the derivatives for simple functions and using these derivatives

as the slope of the given functions.

Example 1: Find the slope of the given straight line, f (x) = 3x – 7 using the derivative method.

In order to find the derivative, we can use the Power rule of the Derivatives:

d(xn)/dx = n * xn-1

We can distribute the derivative to both the terms:

d(3x - 7)/dx -> [ d(3x)/ dx ] - [ d(7)/ dx ]

Using the above formula, we get

3(x1-1) + 0 = 3

Hence the slope or the derivative of the given straight line is 3.

Example 2: Find the slope of the tangent drawn to the given function, f(x) = x2 + 4x at x = 2.

In order to find the derivative, we can use the Power rule of the Derivatives:

d(xn)/dx = n * xn-1

We can distribute the derivative to both the terms:

d(x2 + 4x)/dx -> [ d(x2)/ dx ] + [ d(4x)/ dx ]

Using the above formula, we get

2(x2-1) + 4(x1-1) = 2x + 4

Hence the slope is = 2x + 4.

When x = 2, the slope = 2(2) + 4 = 4 + 4 = 8

Hence the slope of the tangent to the curve at x = 2 is 8.