# Thread: Questions regarding Trig. Derivatives

1. ## Questions regarding Trig. Derivatives

Hello, I am trying to find the second derivative of $\displaystyle 7 secx$, and If I did it correctly, I got $\displaystyle 7(sec^3x+secxtan^2x)$

I also have another question, I think I need to do the product rule, but I have to find the first derivative of $\displaystyle 9x^2 sinx + 18 cosx -18 sinx$ 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 $\displaystyle 7\sec{x}$ 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: $\displaystyle 9x^2cosx+18xsinx+18sinx-cosx$ ?

4. not quite, note the last two terms ...

$\displaystyle \frac{d}{dx}(9x^2\sin{x} + 18\cos{x} - 18\sin{x}) =$

$\displaystyle 9x^2\cos{x} + 18x\sin{x} - 18\sin{x} - 18\cos{x}$

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?

$\displaystyle \frac{d}{dx} [k \cdot f(x)] = k \cdot f'(x)$

so ...

$\displaystyle \frac{d}{dx} [-18\sin{x}] = -18 \cdot \cos{x}$

7. ohh, yeah I forget about that rule, doenst seem to be used much - maybe cause I miss it when doing a problem?