Find the derivative of $LaTeX: \displaystyle f(x) = 6^{6^{6^{x}}}$

Taking the derivative with the chain rule gives $LaTeX: \displaystyle f'(x) = \frac{df}{du}\frac{du}{dv}\frac{dv}{dx}$ . $LaTeX: \displaystyle f'(x) = (6^{u} \ln{\left(6 \right)})(6^{v} \ln{\left(6 \right)})(6^{x} \ln{\left(6 \right)})$ . Substituting back in $LaTeX: \displaystyle u$ and $LaTeX: \displaystyle v$ gives $LaTeX: \displaystyle f'(x) = 6^{6^{v}} 6^{v} 6^{x} \ln{\left(6 \right)}^{3} = 6^{6^{6^{x}}} 6^{6^{x}} 6^{x} \ln{\left(6 \right)}^{3}$ .