If the y=8^log2^x, then (d^2y)/(dx^2) is :

The correct answer is Option (4) → $6x$

Using property of exponents

$a^{\log_bx}=x^{\log_ba}$

$∴y=8^{\log_2x}=x^{\log_28}$

$y=x^3$   $(∵\log_28=3)$

Differentiate,

$\frac{dy}{dx}=3x^2$

Differentiating again,

$\frac{d^2y}{dx^2}=\frac{d}{dx}(3x^2)$

$=6x$