# 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?
The text passage contains multiple questions and answers related to trigonometric derivatives and the application of derivative rules.
multiple_questions_with_answers
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>
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- MULTIPLE_QUESTIONS
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# 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?
user
The text passage contains multiple questions and answers related to trigonometric derivatives and the application of derivative rules.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS