Question

If y = `root 3 (a^2 + x^2)` then `dy/dx` = ______

Options

• `2/3x(a^2 + x^2)^((−2)/3)`

• `2/3x(a^2 + x^2)^(2/3)`

• `2/3(a^2 + x^2)^((−2)/3)`

• `2/3(a^2 + x^2)^(2/3)`

Answer 1

If y = `root 3 (a^2 + x^2)` then `dy/dx` = `bbunderline(2/3x(a^2 + x^2)^((−2)/3))`

Explanation:

y = `root3(a2 + x2)​ = (a^2 + x^2)^(1/3)`

`dy/dx = 1/3 (a^2 + x^2)^((−2)/3) xx 2x`

`dy/dx = 2/3x (a^2 + x^2)^((−2)/3)`