Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
y = {x^5} + {x^4} - {x^3} + {x^2} - x + 17\\
\Rightarrow y' = 5{x^4} + 4{x^3} - 3{x^2} + 2x - 1\\
b,\\
y = {x^5} + 17{x^4} - {x^3} + 17{x^2} - 17x - 17\\
\Rightarrow y' = 5{x^4} + 17.4{x^3} - 3{x^2} + 17.2x - 17\\
= 5{x^4} + 68{x^3} - 3{x^2} + 34x - 17\\
c,\\
f\left( x \right) = \left( {x + 17} \right)\left( {{x^3} + {x^2} + x - 17} \right)\\
\Rightarrow f'\left( x \right) = \left( {x + 17} \right)'.\left( {{x^3} + {x^2} + x - 17} \right) + \left( {x + 17} \right)\left( {{x^3} + {x^2} + x - 17} \right)'\\
= 1.\left( {{x^3} + {x^2} + x - 17} \right) + \left( {x + 17} \right)\left( {3{x^2} + 2x + 1} \right)\\
= {x^3} + {x^2} + x - 17 + 3{x^3} + 2{x^2} + x + 51{x^2} + 34x + 17\\
= 4{x^3} + 3{x^2} + 36x\\
d,\\
y = \frac{{x - 17}}{{x - 17}} = 1\\
\Rightarrow y' = 0
\end{array}\)
