# Thread: Derivatives and tangent line

1. ## Derivatives and tangent line

1. Find the derivative of $\displaystyle cos(sin(x^2))$

2. Find the derivative of $\displaystyle (4 tan(x))/x$

3. Find the equation of the tangent line to the curve $\displaystyle y=3 tan(x)$ at the point $\displaystyle ((pi/4) , 3)$

2. gotta redeem myself from my mistake earlier

ok *cracks fingers*

open the thumbnail in a new window

so yah refresh me, tangent line is the first derivative to find the slope then plugged into point-slope form?

3. ## Reply

1

4. Originally Posted by ryukolink
gotta redeem myself from my mistake earlier

ok *cracks fingers*

open the thumbnail in a new window

so yah refresh me, tangent line is the first derivative to find the slope then plugged into point-slope form?
Yeah I think so.

The first one worked great, thanks. With the second one though, I can't tell if it was $\displaystyle 4sec^2x(x)^-1$ or $\displaystyle 4sec^2(x)^-1$ Which is it?

5. argh! I'm sorry I forgot to put another (x) after sec^2, damn my fast typing.. the correct one is $\displaystyle 4sec^2x(x)^-1$

6. Originally Posted by ryukolink
argh! I'm sorry I forgot to put another (x) after sec^2, damn my fast typing
Oh ok that makes sense. It works now, thanks!

7. ey calculus is a hard mother, no problem man

8. Originally Posted by Shyam
3. equation of curve, $\displaystyle y = 3 \tan x$

slope of tangent, $\displaystyle \frac{dy}{dx}=3 \sec^2 x$

$\displaystyle \left[\frac{dy}{dx}\right]_{(x=\frac{\pi}{4})}=3 \sec^2 \left(\frac{\pi}{4} \right)$

$\displaystyle slope=\left[{\frac{dy}{dx}}\right]_{(x=\frac{\pi}{4})}= 6$

equation of tangent at $\displaystyle \left( \frac{\pi}{4}, 3 \right)$ is

$\displaystyle x-\frac{\pi}{4}=6(y-3)$

$\displaystyle x-6y+18-\frac{\pi}{4}=0$

$\displaystyle x-6y+\frac{72-\pi}{4}=0$
It's saying that the tangent line one isn't right.... (and sorry to be a hassle, but could you put in in slope-intercept form?)

9. Originally Posted by john11235
It's saying that the tangent line one isn't right.... (and sorry to be a hassle, but could you put in in slope-intercept form?)
You try to put this equation in slpoe-intercept form. You please do not depend completely on others. You solve it , it is easy. And then show your work.

10. Never mind I got it. Thanks guys!