1,cho hs f(x) = log2(x² + 1 ) , f'(1) = ? 2,cho hs f(x) = e ngũ (2x + 1) , f'(1) = ?

1)

$f(x)=\log_2(x^2+1)$

$f'(x)=\dfrac{1}{(x^2+1)\ln2}{(x^2+1)'}=\dfrac{2x}{\ln2(x^2+1)}$

$f'(1)=\dfrac{2}{\ln2.2}=\dfrac{1}{\ln 2}=\dfrac{\ln e}{\ln 2}=\ln\dfrac{e}{2}$

2)

$f(x)=e^{2x+1}$

$f'(x)=2e^{2x+1}$

$f'(1)=2e^3$

Đáp án:

$\begin{array}{l}
1)f\left( x \right) = \log 2\left( {{x^2} + 1} \right)\\
 \Rightarrow f'\left( x \right) = \frac{{2.2x}}{{2\left( {{x^2} + 1} \right).\ln 10}} = \frac{{2x}}{{\left( {{x^2} + 1} \right).\ln 10}}\\
 \Rightarrow f'\left( 1 \right) = \frac{1}{{\ln 10}} = \log e\\
2)\\
f\left( x \right) = {e^{2x + 1}}\\
 \Rightarrow f'\left( x \right) = 2.{e^{2x + 1}}\\
 \Rightarrow f'\left( 1 \right) = 2.{e^3}
\end{array}$