Hướng dẫn giải Bài 5 (Trang 78 SGK Toán Giải Tích 12)

Bài 5 (Trang 78 SGK Toán Giải Tích 12): Tính đạo hàm của các hàm số a) y = 3x2 - ln x + 4.sin x; b) y = log(x2+x+1); c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><msub><mi>log</mi><mn>3</mn></msub><mi mathvariant="normal">x</mi></mrow><mi mathvariant="normal">x</mi></mfrac></math>. Hướng dẫn giải: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mn>3</mn><mi mathvariant="normal">x</mi><mn>2</mn><mo> </mo><mo>-</mo><mo> </mo><mi>ln</mi><mo> </mo><mi mathvariant="normal">x</mi><mo> </mo><mo>+</mo><mo> </mo><mn>4</mn><mo>.</mo><mi>sin</mi><mo> </mo><mi mathvariant="normal">x</mi><mo>)</mo><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mn>3</mn><mi mathvariant="normal">x</mi><mn>2</mn><mo>)</mo><mo>'</mo><mo> </mo><mo>-</mo><mo> </mo><mo>(</mo><mi>ln</mi><mo> </mo><mi mathvariant="normal">x</mi><mo>)</mo><mo>'</mo><mo> </mo><mo>+</mo><mo> </mo><mo>(</mo><mn>4</mn><mo>.</mo><mi>sin</mi><mo> </mo><mi mathvariant="normal">x</mi><mo>)</mo><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mn>6</mn><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><mfrac><mn>1</mn><mi mathvariant="normal">x</mi></mfrac><mo> </mo><mo>+</mo><mo> </mo><mn>4</mn><mo>.</mo><mi>cos</mi><mo> </mo><mi mathvariant="normal">x</mi></math>. b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mfenced open="[" close="]"><mrow><mi>log</mi><mfenced><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mi mathvariant="normal">x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfenced><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mfenced><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mi mathvariant="normal">x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>'</mo></mrow><mrow><mfenced><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mi mathvariant="normal">x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>.</mo><mo> </mo><mi>ln</mi><mn>10</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>2</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>1</mn></mrow><mrow><mfenced><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mi mathvariant="normal">x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>.</mo><mi>ln</mi><mn>10</mn></mrow></mfrac></math>. c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>'</mo><mo> </mo><mo>=</mo><mo> </mo><msup><mfenced><mfrac><mrow><msub><mi>log</mi><mn>3</mn></msub><mi mathvariant="normal">x</mi></mrow><mi mathvariant="normal">x</mi></mfrac></mfenced><mo>'</mo></msup><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><msup><mfenced><mrow><msub><mi>log</mi><mn>3</mn></msub><mi mathvariant="normal">x</mi></mrow></mfenced><mo>'</mo></msup><mo>.</mo><mi mathvariant="normal">x</mi><mo>-</mo><mo>(</mo><mi mathvariant="normal">x</mi><mo>)</mo><mo>'</mo><mo>.</mo><msub><mi>log</mi><mn>3</mn></msub><mi mathvariant="normal">x</mi></mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mstyle displaystyle="true"><mfrac><mn>1</mn><mrow><mi mathvariant="normal">x</mi><mo>.</mo><mi>ln</mi><mo> </mo><mn>3</mn></mrow></mfrac></mstyle><mo>.</mo><mi mathvariant="normal">x</mi><mo> </mo><mo>-</mo><mo> </mo><msub><mi>log</mi><mn>3</mn></msub><mi mathvariant="normal">x</mi></mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mstyle displaystyle="true"><mfrac><mn>1</mn><mrow><mi>ln</mi><mn>3</mn></mrow></mfrac></mstyle><mo>-</mo><msub><mi>log</mi><mn>3</mn></msub><mi mathvariant="normal">x</mi></mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>1</mn><mo>-</mo><mi>ln</mi><mn>3</mn><mo>.</mo><msub><mi>log</mi><mn>3</mn></msub><mi mathvariant="normal">x</mi></mrow><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>.</mo><mi>ln</mi><mn>3</mn></mrow></mfrac><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mn>1</mn><mo>-</mo><mi>ln</mi><mo> </mo><mi mathvariant="normal">x</mi></mrow><mrow><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo> </mo><mo>-</mo><mo> </mo><mi>ln</mi><mn>3</mn></mrow></mfrac></math>.