Question

Find the first derivative of the following:
f(x)=x²​

Answer 1

f'(x) = 2x

Explanation:

Using the power rule

`(d)/(dx)` (a
`x^(n)` ) = na
`x^(n-1)`

f(x) = x²

f'(x) = 2.1
`x^(2-1)` = 2x

Answer 2

`\displaystyle f'(x) = 2 {x}`

Explanation:

we would like to differentiate the following:

`\displaystyle f(x) = {x}^(2)`

take derivative In both sides:

`\displaystyle f'(x) = (d)/(dx) {x}^(2)`

use exponent derivation rule:

`\displaystyle f'(x) = 2 {x}^(2 - 1)`

simplify substraction:

`\displaystyle f'(x) = 2 {x}^(1)`

by law of exponent we obtain:

`\displaystyle f'(x) = 2 {x}`

and we are done!