Derivatives and tangent line

**john11235** · October 19th 2008, 08:00 PM

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

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

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

**ryukolink** · October 19th 2008, 08:22 PM

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?

**Shyam** · October 19th 2008, 08:34 PM

1

**john11235** · October 19th 2008, 08:34 PM

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 $4sec^2x(x)^-1$ or $4sec^2(x)^-1$ Which is it?

**ryukolink** · October 19th 2008, 08:37 PM

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

**john11235** · October 19th 2008, 08:41 PM

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!

**ryukolink** · October 19th 2008, 08:42 PM

ey calculus is a hard mother, no problem man

**john11235** · October 19th 2008, 08:48 PM

Originally Posted by Shyam

3. equation of curve, $y = 3 \tan x$

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

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

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

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

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

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

$x-6y+\frac{72-\pi}{4}=0$

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?)

**Shyam** · October 19th 2008, 09:00 PM

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.

**john11235** · October 19th 2008, 09:02 PM

Never mind I got it. Thanks guys!

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