Đáp án:
$1)
a) y'=1400x^{99}+700x^{49}-28x+14\\
b) y'=1400x^{99}+700x^{49}-28x-7\frac{1}{\sqrt{x}}+14\\
c) f'(x)=(10x^9-7\frac{1}{\sqrt{x}})(x^2-14x+14)+(x^{10}-14\sqrt{x}+14)(2x-14)\\
d) y'=\frac{560}{(14x+20)^2}\\
e) y'=\frac{-420}{(20x-14)^2}\\
f) y'=10.(14x^{20}-14x^7+14x-14)^{9}.(280x^{19}-98x^{6}+14)$
Giải thích các bước giải:
$1)
a) y=14x^{100}+14x^{50}-14x^2+14x-14\\
\Rightarrow y'=\left (14x^{100}+14x^{50}-14x^2+14x-14 \right )'\\
=14.100x^{99}+14.50x^{49}-14.2x+14\\
=1400x^{99}+700x^{49}-28x+14\\
b) y=14x^{100}+14x^{50}-14x^2-14\sqrt{14}+14x-14\\
\Rightarrow y'=\left (14x^{100}+14x^{50}-14x^2-14\sqrt{x}+14x-14 \right )'\\
=14.100x^{99}+14.50x^{49}-14.2x-14.\frac{1}{2\sqrt{x}}+14\\
=1400x^{99}+700x^{49}-28x-7\frac{1}{\sqrt{x}}+14\\
c) f(x)=(x^{10}-14\sqrt{x}+14)(x^2-14x+14)\\
\Rightarrow f'(x)=\left [(x^{10}-14\sqrt{x}+14)(x^2-14x+14) \right ]'
=(x^{10}-14\sqrt{x}+14)'(x^2-14x+14)+(x^{10}-14\sqrt{x}+14)(x^2-14x+14)'\\
=(10x^9-14\frac{1}{2\sqrt{x}})(x^2-14x+14)+(x^{10}-14\sqrt{x}+14)(2x-14)\\
=(10x^9-7\frac{1}{\sqrt{x}})(x^2-14x+14)+(x^{10}-14\sqrt{x}+14)(2x-14)\\
d) y=\frac{14x-10}{14x+20}\\
\Rightarrow y'=\left ( \frac{14x-10}{14x+20} \right )'\\
=\frac{(14x-10)'.(14x+20)-(14x-10).(14x+20)'}{(14x+20)^2}\\
=\frac{14(14x+20)-(14x-10).14}{(14x+20)^2}\\
=\frac{196x+280-196x+140}{(14x+20)^2}\\
=\frac{560}{(14x+20)^2}\\
e) y=\frac{10x+14}{20x-14}\\
\Rightarrow y'=\left ( \frac{10x+14}{20x-14} \right )'\\
=\frac{(10x+14)'.(20x-14)-(10x+14).(20x-14)'}{(20x-14)^2}\\
=\frac{10(20x-14)-(10x+14).20}{(20x-14)^2}\\
=\frac{200x-140-200x-280}{(20x-14)^2}\\
=\frac{-420}{(20x-14)^2}\\
f) y=(14x^{20}-14x^7+14x-14)^{10}\\
\Rightarrow y'=\left [(14x^{20}-14x^7+14x-14)^{10} \right ]'\\
=10.(14x^{20}-14x^7+14x-14)^{10-1}.(14x^{20}-14x^7+14x-14)'\\
=10.(14x^{20}-14x^7+14x-14)^{9}.(14.20x^{20-1}-14.7x^{7-1}+14)\\
=10.(14x^{20}-14x^7+14x-14)^{9}.(280x^{19}-98x^{6}+14)$
