text: # Đạo hàm của $y=\left({x}^{3}-5\right).\sqrt{x}$ là
  
  A.
  
  $y\text{'}=\frac{7}{2}\sqrt{{x}^{5}}-\frac{5}{2\sqrt{x}}$.
  
  B.
  
  $y\text{'}=3{x}^{2}\frac{1}{2\sqrt{x}}$.
  
  C.
  
  $y\text{'}=3{x}^{2}-\frac{5}{2\sqrt{x}}$.
  
  D.
  
  Một kết quả khác.
  
  Đáp án:A
  Lời giải:
  
  $y=\left({x}^{3}-5\right).\sqrt{x}=3{x}^{2}\sqrt{x}+\frac{{x}^{3}-5}{2\sqrt{x}}\phantom{\rule{0ex}{0ex}}=\frac{6{x}^{3}}{2\sqrt{x}}+\frac{{x}^{3}}{2\sqrt{x}}-\frac{5}{2\sqrt{x}}=\frac{7}{2}\sqrt{{x}^{5}}-\frac{5}{2\sqrt{x}}$
explanation: The document contains a math question and its answer. The question asks for the derivative of a given function, and the correct answer is provided along with a detailed solution.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Đạo hàm của $y=\left({x}^{3}-5\right).\sqrt{x}$ là
  
  A.
  
  $y\text{'}=\frac{7}{2}\sqrt{{x}^{5}}-\frac{5}{2\sqrt{x}}$.
  
  B.
  
  $y\text{'}=3{x}^{2}\frac{1}{2\sqrt{x}}$.
  
  C.
  
  $y\text{'}=3{x}^{2}-\frac{5}{2\sqrt{x}}$.
  
  D.
  
  Một kết quả khác.
  
  Đáp án:A
  Lời giải:
  
  $y=\left({x}^{3}-5\right).\sqrt{x}=3{x}^{2}\sqrt{x}+\frac{{x}^{3}-5}{2\sqrt{x}}\phantom{\rule{0ex}{0ex}}=\frac{6{x}^{3}}{2\sqrt{x}}+\frac{{x}^{3}}{2\sqrt{x}}-\frac{5}{2\sqrt{x}}=\frac{7}{2}\sqrt{{x}^{5}}-\frac{5}{2\sqrt{x}}$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its answer. The question asks for the derivative of a given function, and the correct answer is provided along with a detailed solution.
  
  Label: question-and-answer