Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
y = 14{x^{100}} + 14{x^{50}} - 14{x^2} + 14x - 14\\
= 14\left( {{x^{100}} + {x^{50}} - {x^2} + x - 1} \right)\\
\Rightarrow y' = 14.\left( {100{x^{99}} + 50{x^{49}} - 2x + 1} \right)\\
b,\\
y = 14{x^{100}} + 14{x^{50}} - 14{x^2} - 14\sqrt x + 14x - 14\\
= 14\left( {{x^{100}} + {x^{50}} - {x^2} - \sqrt x + x - 1} \right)\\
\Rightarrow y' = 14\left( {100{x^{99}} + 50{x^{49}} - 2x - \frac{1}{{2\sqrt x }} + 1} \right)\\
c,\\
y = \left( {{x^{10}} - 14\sqrt x + 14} \right)\left( {{x^2} - 14x + 14} \right)\\
\Rightarrow y' = \left( {{x^{10}} - 14\sqrt x + 14} \right)'.\left( {{x^2} - 14x + 14} \right) + \left( {{x^{10}} - 14\sqrt x + 14} \right) + \left( {{x^2} - 14x + 14} \right)'\\
\Rightarrow y' = \left( {{x^9} - \frac{7}{{\sqrt x }}} \right)\left( {{x^2} - 14x + 14} \right) + \left( {{x^{10}} - 14\sqrt x + 14} \right).\left( {2x - 14} \right)\\
d,\\
y = \frac{{14x - 10}}{{14x + 20}} = \frac{{7x - 5}}{{7x + 10}}\\
\Rightarrow y' = \frac{{\left( {7x - 5} \right)'.\left( {7x + 10} \right) - \left( {7x + 10} \right)'.\left( {7x - 5} \right)}}{{{{\left( {7x + 10} \right)}^2}}}\\
= \frac{{7.\left( {7x + 10} \right) - 7.\left( {7x - 5} \right)}}{{{{\left( {7x + 10} \right)}^2}}} = \frac{{105}}{{{{\left( {7x + 10} \right)}^2}}}\\
e,\\
y = \frac{{10x + 14}}{{20x - 14}} = \frac{{5x + 7}}{{10x - 7}}\\
\Rightarrow y' = \frac{{\left( {5x + 7} \right)'.\left( {10x - 7} \right) - \left( {5x + 7} \right).\left( {10x - 7} \right)'}}{{{{\left( {10x - 7} \right)}^2}}}\\
= \frac{{5\left( {10x - 7} \right) - 10.\left( {5x + 7} \right)}}{{{{\left( {10x - 7} \right)}^2}}} = \frac{{ - 105}}{{{{\left( {10x - 7} \right)}^2}}}\\
f,\\
y = {\left( {14{x^{20}} - 14{x^7} + 14x - 14} \right)^{10}}\\
\Rightarrow y' = 20.\left( {14{x^{20}} - 14{x^7} + 14x - 14} \right)'.{\left( {14{x^{20}} - 14{x^7} + 14x - 14} \right)^9}\\
= 20.14.\left( {20{x^{19}} - 7{x^6} + 1} \right).{\left( {14{x^{20}} - 14{x^7} + 14x - 14} \right)^9}\\
= {20.14^{10}}.\left( {20{x^{19}} - 7{x^6} + 1} \right).{\left( {{x^{20}} - {x^7} + x - 1} \right)^9}
\end{array}\)
