Question

Find the derivative of -


1.) X³ - 27

2.) 2x²


​

Answer 1

1. X^3 -27

3x^2-0

3x^2 ans.

2. 2x^2

4x Ans.

Answer 2

$<b> <u> Heya! </u>$

___________________________________________________________

$<u> Derivatives </u></b>$

→ First let me explain the rule used :-

=> d/dx ( xⁿ) = nx^(n-1)

⚫$<i> This means that when we differentiate a function w.r.t with some power , the power comes in the front and the power of the variable is decreased by 1.</i>$

________________________________________

1.) x³ - 27

◼$<i> Now derivative for the power , we will use the rule mentioned above . And we know that the derivative of a constant is 0 . </i>$

Therefore we have ,

=> 3 (x)² - 0

=> 3x² ✔

•°• $<u> The derivative of x³ - 27 is 3x² </u>$

________________________________________

2.) 2x²

◼$<i> Now once again , derivative for the power , we will use the rule mentioned above . And here there's no need of any other rule . </i>$

So simply we get ,


=> 2 × 2 x¹

=> 4 × x

=> 4x ✔


•°• $<u> The derivative of 2x² is 4x </u>$


$<i> Thanks !! </i>$
________________________________________