Find the derivative of $LaTeX: \displaystyle f(x) = 9^{2^{8^{x}}}$

Taking the derivative with the chain rule gives $LaTeX: \displaystyle f'(x) = \frac{df}{du}\frac{du}{dv}\frac{dv}{dx}$ . $LaTeX: \displaystyle f'(x) = (9^{u} \ln{\left(9 \right)})(2^{v} \ln{\left(2 \right)})(8^{x} \ln{\left(8 \right)})$ . Substituting back in $LaTeX: \displaystyle u$ and $LaTeX: \displaystyle v$ gives $LaTeX: \displaystyle f'(x) = 2^{v} 8^{x} 9^{2^{v}} \ln{\left(2 \right)} \ln{\left(8 \right)} \ln{\left(9 \right)} = 2^{8^{x}} 8^{x} 9^{2^{8^{x}}} \ln{\left(2 \right)} \ln{\left(8 \right)} \ln{\left(9 \right)}$ .