Chaya Galloway

2021-04-11

Find the derivatives of the following functions.
$f\left(x\right)={x}^{2}{\mathrm{cos}h}^{2}3x$

BleabyinfibiaG

Step 1
The given function is:
$f\left(x\right)={x}^{2}{\mathrm{cos}h}^{2}\left(3x\right)$
We know that,
$d\frac{\mathrm{cos}hx}{dx}=\mathrm{sin}hx$
$d\frac{\mathrm{sin}hx}{dx}=\mathrm{cos}hx$
Step 2
Differentiating the above function with respect to x we get,
$d\frac{f\left(x\right)}{dx}=d\frac{{x}^{2}{\mathrm{cos}h}^{2}\left(3x\right)}{dx}$
$d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+{x}^{2}\left[2\left(3\right)\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)\right]$
$d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+6{x}^{2}\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)$
$d\frac{f\left(x\right)}{dx}=2x\mathrm{cos}h\left(3x\right)\left[\mathrm{cos}h\left(3x\right)+3x\mathrm{sin}h\left(3x\right)\right]$
The text passage contains a mathematical question asking for the derivative of a given function, and it also provides the answer to this question.
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
Chaya Galloway

2021-04-11

Find the derivatives of the following functions.
$f\left(x\right)={x}^{2}{\mathrm{cos}h}^{2}3x$

BleabyinfibiaG

Step 1
The given function is:
$f\left(x\right)={x}^{2}{\mathrm{cos}h}^{2}\left(3x\right)$
We know that,
$d\frac{\mathrm{cos}hx}{dx}=\mathrm{sin}hx$
$d\frac{\mathrm{sin}hx}{dx}=\mathrm{cos}hx$
Step 2
Differentiating the above function with respect to x we get,
$d\frac{f\left(x\right)}{dx}=d\frac{{x}^{2}{\mathrm{cos}h}^{2}\left(3x\right)}{dx}$
$d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+{x}^{2}\left[2\left(3\right)\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)\right]$
$d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+6{x}^{2}\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)$
$d\frac{f\left(x\right)}{dx}=2x\mathrm{cos}h\left(3x\right)\left[\mathrm{cos}h\left(3x\right)+3x\mathrm{sin}h\left(3x\right)\right]$
user
The text passage contains a mathematical question asking for the derivative of a given function, and it also provides the answer to this question.

TYPE: SINGLE_QUESTION_WITH_ANSWER