text: # Thread: Questions regarding Trig. Derivatives
  
  1. ## Questions regarding Trig. Derivatives
  
  Hello, I am trying to find the second derivative of $7 secx$, and If I did it correctly, I got $7(sec^3x+secxtan^2x)$
  
  I also have another question, I think I need to do the product rule, but I have to find the first derivative of $9x^2 sinx + 18 cosx -18 sinx$ Im not sure how to go about using the product rule with this, as there is like 3 terms. Any help would be appreciated, Thanks!
  
  2. your 2nd derivative for $7\sec{x}$ is correct.
  
  for the second problem, use the product rule for the first term only ... take the derivative of the last two terms as usual.
  
  3. Ok, thanks!
  
  hmmm, so the first derivative of ,
  
  would be: $9x^2cosx+18xsinx+18sinx-cosx$ ?
  
  4. not quite, note the last two terms ...
  
  $\frac{d}{dx}(9x^2\sin{x} + 18\cos{x} - 18\sin{x}) =$
  
  $9x^2\cos{x} + 18x\sin{x} - 18\sin{x} - 18\cos{x}$
  
  5. haha, wow, thats what I had written on my paper, but I typed it wrong.
  
  edit: wait, doesnt the 18 in the last term go to 0, thats where I wrote -cosx, cause you took teh deriv, of the middle term, but when u take the deriv of the last term -18sinx should it go to -cosx, since deriv of -18 is 0
  
  6. remember the constant multiple rule?
  
  $\frac{d}{dx} [k \cdot f(x)] = k \cdot f'(x)$
  
  so ...
  
  $\frac{d}{dx} [-18\sin{x}] = -18 \cdot \cos{x}$
  
  7. ohh, yeah I forget about that rule, doenst seem to be used much - maybe cause I miss it when doing a problem?
explanation: The document is a discussion thread about trigonometric derivatives. It contains multiple questions and answers related to finding the second derivative of \(7 \sec x\) and the first derivative of \(9x^2 \sin x + 18 \cos x - 18 \sin x\). The user asks for help, and another user provides feedback and corrections.
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: # Thread: Questions regarding Trig. Derivatives
  
  1. ## Questions regarding Trig. Derivatives
  
  Hello, I am trying to find the second derivative of $7 secx$, and If I did it correctly, I got $7(sec^3x+secxtan^2x)$
  
  I also have another question, I think I need to do the product rule, but I have to find the first derivative of $9x^2 sinx + 18 cosx -18 sinx$ Im not sure how to go about using the product rule with this, as there is like 3 terms. Any help would be appreciated, Thanks!
  
  2. your 2nd derivative for $7\sec{x}$ is correct.
  
  for the second problem, use the product rule for the first term only ... take the derivative of the last two terms as usual.
  
  3. Ok, thanks!
  
  hmmm, so the first derivative of ,
  
  would be: $9x^2cosx+18xsinx+18sinx-cosx$ ?
  
  4. not quite, note the last two terms ...
  
  $\frac{d}{dx}(9x^2\sin{x} + 18\cos{x} - 18\sin{x}) =$
  
  $9x^2\cos{x} + 18x\sin{x} - 18\sin{x} - 18\cos{x}$
  
  5. haha, wow, thats what I had written on my paper, but I typed it wrong.
  
  edit: wait, doesnt the 18 in the last term go to 0, thats where I wrote -cosx, cause you took teh deriv, of the middle term, but when u take the deriv of the last term -18sinx should it go to -cosx, since deriv of -18 is 0
  
  6. remember the constant multiple rule?
  
  $\frac{d}{dx} [k \cdot f(x)] = k \cdot f'(x)$
  
  so ...
  
  $\frac{d}{dx} [-18\sin{x}] = -18 \cdot \cos{x}$
  
  7. ohh, yeah I forget about that rule, doenst seem to be used much - maybe cause I miss it when doing a problem?
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a discussion thread about trigonometric derivatives. It contains multiple questions and answers related to finding the second derivative of \(7 \sec x\) and the first derivative of \(9x^2 \sin x + 18 \cos x - 18 \sin x\). The user asks for help, and another user provides feedback and corrections.
  
  Label: multiple-question-and-answer