Bài 4: Hàm số mũ. Hàm số lôgarit
<span data-v-a7c68f28="">Hướng dẫn giải Hoạt động 3 (Trang 75 SGK Toán Giải Tích 12)</span>
<p><strong class="content_question">Đề bài</strong></p>
<p>Tìm đạo hàm của hàm số: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>ln</mi><mfenced><mrow><mi>x</mi><mo>+</mo><msqrt><mfenced><mrow><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced></msqrt></mrow></mfenced></math></p>
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<p class="content_method_header"><strong class="content_method">Phương pháp giải - Xem chi tiết</strong><img id="method_colapse_icon" class="method-open-icon" src="data:image/png;base64,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" /></p>
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<p>Sử dụng công thức đạo hàm <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mfenced><mi>u</mi></mfenced><mo>'</mo><mo>=</mo><mfrac><mrow><mi>u</mi><mo>'</mo></mrow><mi>u</mi></mfrac></math></p>
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<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>'</mo><mo>=</mo><mfenced open="[" close="]"><mrow><mi>ln</mi><mfenced><mrow><mi>x</mi><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mrow></mfenced></mrow></mfenced><mo>'</mo><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mrow></mfenced><mo>'</mo></mrow><mrow><mi>x</mi><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mrow><mfenced><mrow><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mo>'</mo></mrow><mrow><mn>2</mn><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mrow></mfrac></mstyle></mrow><mrow><mi>x</mi><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>x</mi></mrow><mrow><mn>2</mn><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mrow></mfrac></mstyle></mrow><mrow><mi>x</mi><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mi>x</mi><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mfrac></mstyle></mrow><mrow><mi>x</mi><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt><mo>+</mo><mi>x</mi></mrow><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mfrac></mstyle><mrow><mi>x</mi><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>1</mn><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></msqrt></mfrac><mspace linebreak="newline"/></math><br /><span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt></mrow></mfrac></mstyle></math>"><span id="MJXc-Node-308" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-309" class="mjx-mrow"><span id="MJXc-Node-311" class="mjx-mstyle MJXc-space3"><span id="MJXc-Node-312" class="mjx-mrow"><span id="MJXc-Node-313" class="mjx-mfrac"><span class="mjx-box MJXc-stacked"><span class="mjx-denominator"><span id="MJXc-Node-315" class="mjx-texatom"><span id="MJXc-Node-316" class="mjx-mrow"><span id="MJXc-Node-317" class="mjx-msqrt"><span class="mjx-box"><span id="MJXc-Node-318" class="mjx-mrow"><span id="MJXc-Node-321" class="mjx-texatom MJXc-space2"><span id="MJXc-Node-322" class="mjx-mrow"><span id="MJXc-Node-323" class="mjx-msubsup"><span class="mjx-sup"><span id="MJXc-Node-325" class="mjx-mn"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p>
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