Answer
$\dfrac{12x^2}{(1+16x^6)^{3/2}}$
Work Step by Step
Given: $y=x^4$
Consider $f(x)=y=x^4$
In order to find the curvature we will have to use formula 11, such that
$\kappa(x)=\dfrac{|f''(x)|}{[1+(f'(x))^2]^{3/2}}$
$y'=4x^3$ and $y''=12x^2$
$|y''|=\sqrt{(12x^2)^2}=12x^2$
$\kappa(x)=\dfrac{|12x^2|}{[1+(4x^3))^2]^{3/2}}$
Hence, $\kappa(x)=\dfrac{12x^2}{(1+16x^6)^{3/2}}$