# 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:

$y=\left({x}^{3}-5\right).\sqrt{x}=3{x}^{2}\sqrt{x}+\frac{{x}^{3}-5}{2\sqrt{x}}\phantom{\rule{0ex}{0ex}}=\frac{6{x}^{3}}{2\sqrt{x}}+\frac{{x}^{3}}{2\sqrt{x}}-\frac{5}{2\sqrt{x}}=\frac{7}{2}\sqrt{{x}^{5}}-\frac{5}{2\sqrt{x}}$
The passage contains a mathematical question asking for the derivative of a given function, followed by multiple-choice answers and the correct answer with an explanation.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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:

$y=\left({x}^{3}-5\right).\sqrt{x}=3{x}^{2}\sqrt{x}+\frac{{x}^{3}-5}{2\sqrt{x}}\phantom{\rule{0ex}{0ex}}=\frac{6{x}^{3}}{2\sqrt{x}}+\frac{{x}^{3}}{2\sqrt{x}}-\frac{5}{2\sqrt{x}}=\frac{7}{2}\sqrt{{x}^{5}}-\frac{5}{2\sqrt{x}}$
user
The passage contains a mathematical question asking for the derivative of a given function, followed by multiple-choice answers and the correct answer with an explanation.

TYPE: SINGLE_QUESTION_WITH_ANSWER