$\lim_{x\to0}\left(1+\left(\left(\left(\left(a^2\right)^2\right)^2\right)^2\right)^2-\left(a^2\right)^2\right)=1+a^{32}-a^{4}$
See step-by-step solution
Derivative of this function
$\frac{d}{da}\left(1+\left(\left(\left(\left(a^2\right)^2\right)^2\right)^2\right)^2-\left(a^2\right)^2\right)=32a^{31}-4a^{3}$
See step-by-step solution
Integral of this function
$\int\left(1+\left(\left(\left(\left(a^2\right)^2\right)^2\right)^2\right)^2-\left(a^2\right)^2\right)da=a+a^{33}-a^{5}+C_0$
See step-by-step solution