1) (-6x):(2х)=-3
2) (-6ху):(-3ху)=2
3) 8abc:(-4a)=-2bc
4)14a в пятой степени :(-4а)=-3,5a^6
5)-0.2а в 10 степени :(-а в 10 степени)=0,2
<span>Дана система ур-ний</span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>+</span><span>y<span /></span><span>=</span><span>2</span></span><span /></span></span><span /></span><span>3x+y=2</span></span>
<span /><span><span><span><span><span><span>2</span><span>x</span><span>−</span><span>y<span /></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>2x−y=3</span></span>
<span>Из 1-го ур-ния выразим x</span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>+</span><span>y<span /></span><span>=</span><span>2</span></span><span /></span></span><span /></span><span>3x+y=2</span></span>
<span>Перенесем слагаемое с переменной y из левой части в правую со сменой знака</span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>=</span><span>−</span><span>y<span /></span><span>+</span><span>2</span></span><span /></span></span><span /></span><span>3x=−y+2</span></span>
<span /><span><span><span><span><span><span>3</span><span>x</span><span>=</span><span>−</span><span>y<span /></span><span>+</span><span>2</span></span><span /></span></span><span /></span><span>3x=−y+2</span></span>
<span>Разделим обе части ур-ния на множитель при x</span>
<span /><span><span><span><span><span><span><span><span><span><span>3</span><span>x</span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>1</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span><span>(</span><span>−</span><span>y<span /></span><span>+</span><span>2</span><span>)</span></span></span><span /></span></span><span /></span><span>3x3=13(−y+2)</span></span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>−</span><span><span><span><span>y<span /></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>x=−y3+23</span></span>
<span>Подставим найденное x в 2-е ур-ние</span>
<span /><span><span><span><span><span><span>2</span><span>x</span><span>−</span><span>y<span /></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>2x−y=3</span></span>
<span>Получим:</span>
<span /><span><span><span><span><span><span>−</span><span>y<span /></span><span>+</span><span>2</span><span><span><span>(</span></span><span>−</span><span><span><span><span>y<span /></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span><span>)</span></span></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>−y+2(−y3+23)=3</span></span>
<span /><span><span><span><span><span><span>−</span><span><span><span><span><span>5</span><span>y<span /></span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>4</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span>3</span></span><span /></span></span><span /></span><span>−5y3+43=3</span></span>
<span>Перенесем свободное слагаемое 4/3 из левой части в правую со сменой знака</span>
<span /><span><span><span><span><span><span>−</span><span><span><span><span><span>5</span><span>y<span /></span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>−5y3=53</span></span>
<span /><span><span><span><span><span><span>−</span><span><span><span><span><span>5</span><span>y<span /></span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>=</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>−5y3=53</span></span>
<span>Разделим обе части ур-ния на множитель при y</span>
<span /><span><span><span><span><span><span><span><span><span><span>−</span><span>1</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>y<span /></span></span><span /></span><span><span><span>−</span><span><span><span><span>5</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span><span><span /><span /></span></span></span><span>=</span><span>−</span><span>1</span></span><span /></span></span><span /></span><span>−153y−53=−1</span></span>
<span /><span><span><span><span><span><span>y<span /></span><span>=</span><span>−</span><span>1</span></span><span /></span></span><span /></span><span>y=−1</span></span>
<span>Т.к.</span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>−</span><span><span><span><span>y<span /></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>x=−y3+23</span></span>
<span>то</span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>−</span><span><span><span><span><span>−</span><span>1</span></span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span><span>+</span><span><span><span><span>2</span><span /></span><span><span>3</span><span /></span><span><span /><span /></span></span></span></span><span /></span></span><span /></span><span>x=−−13+23</span></span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>1</span></span><span /></span></span><span /></span><span>x=1</span></span>
<span>Ответ:</span>
<span /><span><span><span><span><span><span>x</span><span>=</span><span>1</span></span><span /></span></span><span /></span><span>x=1</span></span>
<span /><span><span><span><span><span><span>y<span /></span><span>=</span><span>−</span><span>1</span></span><span /></span></span><span /></span></span><span>
</span>
Производная сумма равна сумме производных
y' = 9x^8+1/3+5/x
