Question

A derivada de y=x¹⁰⁰⁰​

Answer 1

Olá,

Use a regra da potência que versa:

$\boxed{ \tt \: y = {x}^{n} \to \: \dfrac{dy}{dx} = n \: {y}^{ n- 1} }$

Assim, sendo:

$\tt \: y = {x}^{1000} \\ \\ \tt \: \frac{dy}{dx} = 1000 {x}^{1000 - 1} \\ \\ \boxed{\tt \: \frac{dy}{dx} = 1000 {x}^{999} } \: \checkmark$

Answer 2

$\text y = \text x ^{1000}$

derivando :

$\text {y '} = 1000.\text x^{(1000-1)}$

$\huge\boxed{\text {y '} = 1000. \text x^{999}}\checkmark$