text: 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,
  $d\frac{f\left(x\right)}{dx}=d\frac{{x}^{2}{\mathrm{cos}h}^{2}\left(3x\right)}{dx}$
  $d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+{x}^{2}\left[2\left(3\right)\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)\right]$
  $d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+6{x}^{2}\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)$
  $d\frac{f\left(x\right)}{dx}=2x\mathrm{cos}h\left(3x\right)\left[\mathrm{cos}h\left(3x\right)+3x\mathrm{sin}h\left(3x\right)\right]$
explanation: The document contains a math question and its corresponding answer. The question asks for the derivative of the function \( f(x) = x^2 \cosh^2(3x) \). The answer provides a step-by-step solution to find the derivative of the given function.
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: 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,
  $d\frac{f\left(x\right)}{dx}=d\frac{{x}^{2}{\mathrm{cos}h}^{2}\left(3x\right)}{dx}$
  $d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+{x}^{2}\left[2\left(3\right)\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)\right]$
  $d\frac{f\left(x\right)}{dx}=2x{\mathrm{cos}h}^{2}\left(3x\right)+6{x}^{2}\mathrm{cos}h\left(3x\right)\mathrm{sin}h\left(3x\right)$
  $d\frac{f\left(x\right)}{dx}=2x\mathrm{cos}h\left(3x\right)\left[\mathrm{cos}h\left(3x\right)+3x\mathrm{sin}h\left(3x\right)\right]$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding answer. The question asks for the derivative of the function \( f(x) = x^2 \cosh^2(3x) \). The answer provides a step-by-step solution to find the derivative of the given function.
  
  Label: question-and-answer