Cho \(f\left( x \right) = {2.3^{{{\log }_{81}}x}} + 3\). Tính \(f(1)\).

* Hướng dẫn giải

TXĐ: \(D = \left( {0; + \infty } \right)\)

\(\begin{array}{l}
f'\left( x \right) = {2.3^{{{\log }_{81}}x}}.\ln 3.{\left( {{{\log }_{81}}x} \right)^\prime } = {2.3^{{{\log }_{81}}x}}.\ln 3.\frac{1}{{x\ln 81}}\\
f'\left( 1 \right) = {2.3^0}.\ln 3.\frac{1}{{\ln 81}} = 2.1.\ln 3.\frac{1}{{4\ln 3}} = \frac{1}{2}
\end{array}\)