DERIVATIVE BY FIRST PRINCIPLE

Find the derivative of each of the following by first principle.

Example 1 :

xⁿ 

(n is a constant)

Solution :

Let f(x) = xⁿ.

Derivative of xⁿ by first principle :

Example 2 :

3x - 5

Solution :

Let f(x) = 3x - 5.

Derivative of (3x - 5) by first principle :

Example 3 :

2x² - 5x + 4

Solution :

Let f(x) = 2x² - 5x + 4.

Derivative of (2x² - 5x + 4) by first principle :

Example 4 :

e^x

Solution :

Let f(x) = e^x.

Derivative of e^x by first principle :

Example 5 :

f(x) = logx

Solution :

Let f(x) = logx.

Derivative of logx by first principle :

Example 6 :

¹⁄ₓ

Solution :

Let f(x) = ¹⁄ₓ.

Derivative of ¹⁄ₓ by first principle :

Example 7 :

sinx

Solution :

Let f(x) = sinx.

Derivative of sinx by first principle :

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