Hướng dẫn giải Bài 1 (Trang 176 SGK Toán Đại số & Giải tích 11)

Tìm các đạo hàm sau: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><msup><mi>x</mi><mn>3</mn></msup><mn>3</mn></mfrac><mo>-</mo><mfrac><msup><mi>x</mi><mn>2</mn></msup><mn>2</mn></mfrac><mo>+</mo><mi>x</mi><mo>-</mo><mn>5</mn><mspace linebreak="newline"/><mi>b</mi><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mn>2</mn><mi>x</mi></mfrac><mo>-</mo><mfrac><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>5</mn><msup><mi>x</mi><mn>3</mn></msup></mfrac><mo>-</mo><mfrac><mn>6</mn><mrow><mn>7</mn><msup><mi>x</mi><mn>4</mn></msup></mrow></mfrac><mspace linebreak="newline"/><mi>c</mi><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>4</mn><mi>x</mi></mrow></mfrac><mspace linebreak="newline"/><mi>d</mi><mo>,</mo><mi>y</mi><mo>=</mo><mfenced><mrow><mfrac><mn>2</mn><mi>x</mi></mfrac><mo>+</mo><mn>3</mn><mi>x</mi></mrow></mfenced><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>-</mo><mn>1</mn></mrow></mfenced><mspace linebreak="newline"/><mi>e</mi><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mi>x</mi></msqrt></mrow><mrow><mn>1</mn><mo>-</mo><msqrt><mi>x</mi></msqrt></mrow></mfrac><mspace linebreak="newline"/><mi>f</mi><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>7</mn><mi>x</mi><mo>+</mo><mn>5</mn></mrow><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi></mrow></mfrac></math> Giải  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo> </mo><mi>y</mi><mo>'</mo><mo>=</mo><mfenced><mfrac><msup><mi>x</mi><mn>3</mn></msup><mn>3</mn></mfrac></mfenced><mo>'</mo><mo>-</mo><mfenced><mfrac><msup><mi>x</mi><mn>2</mn></msup><mn>2</mn></mfrac></mfenced><mo>'</mo><mo>+</mo><mfenced><mi>x</mi></mfenced><mo>'</mo><mo>-</mo><mfenced><mn>5</mn></mfenced><mo>'</mo><mo>=</mo><mfrac><mrow><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mn>2</mn></mfrac><mo>+</mo><mn>1</mn><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>,</mo><mi>y</mi><mo>'</mo><mo>=</mo><mfenced><mfrac><mn>2</mn><mi>x</mi></mfrac></mfenced><mo>'</mo><mo>-</mo><mfenced><mfrac><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mfenced><mo>'</mo><mo>+</mo><mfenced><mfrac><mn>5</mn><msup><mi>x</mi><mn>3</mn></msup></mfrac></mfenced><mo>'</mo><mo>-</mo><mfenced><mfrac><mn>6</mn><mrow><mn>7</mn><msup><mi>x</mi><mn>4</mn></msup></mrow></mfrac></mfenced><mo>'</mo><mo>=</mo><mo>-</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mfenced><mi>x</mi></mfenced><mo>'</mo></mrow><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mrow><mn>4</mn><mfenced><msup><mi>x</mi><mn>2</mn></msup></mfenced><mo>'</mo></mrow><msup><mi>x</mi><mn>4</mn></msup></mfrac><mo>-</mo><mfrac><mrow><mn>5</mn><mo>.</mo><mfenced><msup><mi>x</mi><mn>3</mn></msup></mfenced><mo>'</mo></mrow><msup><mi>x</mi><mn>6</mn></msup></mfrac><mo>+</mo><mfrac><mn>6</mn><mn>7</mn></mfrac><mo>.</mo><mfrac><mrow><mfenced><msup><mi>x</mi><mn>4</mn></msup></mfenced><mo>'</mo></mrow><msup><mi>x</mi><mn>8</mn></msup></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mrow><mn>4</mn><mo>.</mo><mn>2</mn><mi>x</mi></mrow><msup><mi>x</mi><mn>4</mn></msup></mfrac><mo>-</mo><mfrac><mrow><mn>5</mn><mo>.</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><msup><mi>x</mi><mn>6</mn></msup></mfrac><mo>+</mo><mfrac><mn>6</mn><mn>7</mn></mfrac><mo>.</mo><mfrac><mrow><mn>4</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><msup><mi>x</mi><mn>8</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>8</mn><msup><mi>x</mi><mn>3</mn></msup></mfrac><mo>-</mo><mfrac><mn>15</mn><msup><mi>x</mi><mn>4</mn></msup></mfrac><mo>+</mo><mfrac><mn>24</mn><mrow><mn>7</mn><msup><mi>x</mi><mn>5</mn></msup></mrow></mfrac><mspace linebreak="newline"/><mi>c</mi><mo>,</mo><mi>y</mi><mo>'</mo><mo>=</mo><mfenced><mfrac><mrow><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>7</mn></mrow><mrow><mn>4</mn><mi>x</mi></mrow></mfrac></mfenced><mo>=</mo><mfenced><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>x</mi><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>7</mn><mrow><mn>4</mn><mi>x</mi></mrow></mfrac></mrow></mfenced><mo>=</mo><mfenced><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>x</mi></mrow></mfenced><mo>'</mo><mo>-</mo><mfenced><mfrac><mn>3</mn><mn>2</mn></mfrac></mfenced><mo>'</mo><mo>+</mo><mfenced><mfrac><mn>7</mn><mrow><mn>4</mn><mi>x</mi></mrow></mfrac></mfenced><mo>'</mo><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>-</mo><mn>0</mn><mo>-</mo><mfrac><mn>7</mn><mrow><mn>4</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>-</mo><mfrac><mn>7</mn><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>,</mo><mo> </mo><mi>y</mi><mo>'</mo><mo>=</mo><mfenced open="[" close="]"><mrow><mfenced><mrow><mfrac><mn>2</mn><mi>x</mi></mfrac><mo>+</mo><mn>3</mn><msqrt><mi>x</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>-</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>'</mo><mo>=</mo><mfenced><mrow><mfrac><mn>2</mn><mi>x</mi></mfrac><mo>+</mo><mn>3</mn><msqrt><mi>x</mi></msqrt></mrow></mfenced><mo>'</mo><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>-</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mfrac><mn>2</mn><mi>x</mi></mfrac><mo>+</mo><mn>3</mn><msqrt><mi>x</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>-</mo><mn>1</mn></mrow></mfenced><mo>'</mo><mspace linebreak="newline"/><mo>=</mo><mfenced><mrow><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt></mrow></mfrac></mrow></mfenced><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>-</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mfrac><mn>2</mn><mi>x</mi></mfrac><mo>+</mo><mn>3</mn><msqrt><mi>x</mi></msqrt></mrow></mfenced><mo>.</mo><mfrac><mn>1</mn><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn></mrow><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>-</mo><mfrac><mn>3</mn><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>-</mo><mfrac><mn>3</mn><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt></mrow></mfrac><mo>+</mo><mn>3</mn><mspace linebreak="newline"/><mi>e</mi><mo>,</mo><mo> </mo><mi>y</mi><mo>'</mo><mo>=</mo><mfenced><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mi>x</mi></msqrt></mrow><mrow><mn>1</mn><mo>-</mo><msqrt><mi>x</mi></msqrt></mrow></mfrac></mfenced><mo>'</mo><mo>=</mo><mfenced><mrow><mfrac><mn>2</mn><mrow><mn>1</mn><mo>-</mo><msqrt><mi>x</mi></msqrt></mrow></mfrac><mo>-</mo><mn>1</mn></mrow></mfenced><mo>'</mo><mo>=</mo><mfenced><mfrac><mn>2</mn><mrow><mn>1</mn><mo>-</mo><msqrt><mi>x</mi></msqrt></mrow></mfrac></mfenced><mo>'</mo><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mfenced><mrow><mn>1</mn><mo>-</mo><msqrt><mi>x</mi></msqrt></mrow></mfenced></mrow><msup><mfenced><mrow><mn>1</mn><mo>-</mo><msqrt><mi>x</mi></msqrt></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><mo>.</mo><mfenced><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt></mrow></mfrac></mstyle></mfenced></mrow><msup><mfenced><mrow><mn>1</mn><mo>-</mo><msqrt><mi>x</mi></msqrt></mrow></mfenced><mn>2</mn></msup></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mi>x</mi></msqrt><msup><mfenced><mrow><mn>1</mn><mo>-</mo><msqrt><mi>x</mi></msqrt></mrow></mfenced><mn>2</mn></msup></mrow></mfrac><mspace linebreak="newline"/><mi>f</mi><mo>'</mo><mo> </mo><mi>y</mi><mo>'</mo><mo>=</mo><mfrac><mrow><mo>-</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>10</mn><mi>x</mi><mo>+</mo><mn>15</mn></mrow><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi></mrow></mfenced><mn>2</mn></msup></mfrac></math>

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