Question

como calcular a derivada de y=3^2-5√ x+7(^3√x^2)?

Answer 1

3x² - 5√x + 7∛x²
3x² - 5 x^1/2 + 7(x²)^1/3
6x - 5/2 x^-1/2 + 7/3x^-2/3

Answer 2

y = 3x² - 5√x + 7∛x²


Reescrevendo a função:

y = 3x² - 5.(x^(1/2)) + 7.(x^(2/3))

Derivando:

y' = 6x - 5.(1/2 . x^(1/2 - 1)) + 7.(2/3 . x^(2/3 - 1))

y' = 6x - 5.(1/2 . x^(-1/2)) + 7.(2/3 . x^(-1/3))

y' = 6x - 5.(1/2 . 1/√x) + 7.(2/3 . 1/x^(1/3))

y' = 6x - 5.(1/2√x) + 7.(2/3 . 1/∛x)

y' = 6x - 5.(1/2√x) + 7.(2/3∛x)

y' = 6x - 5/2√x + 14/3∛x


$y' = 6x - \frac{5}{2\sqrt{x}} + \frac{14}{3\sqrt[3]{x}}$