Question

L̶o̶g̶a̶r̶i̶t̶h̶m̶i̶c̶ ̶D̶i̶f̶f̶e̶r̶e̶n̶t̶i̶a̶t̶i̶o̶n̶ Derivatives of Trigonometric Functions
Differentiate the following functions.
LaTeX below.

Answer 1

\[G(x)=\frac{e^{x}-\tan{x}}{\sin{x}+3}\]

Answer 2

\[G'(x)=\frac{(e^{x}-\tan{x})'(\sin{x}+3)-(e^{x}-\tan{x})(\sin{x}+3)'}{(\sin{x}+3)^{2}}\]

Answer 3

\[G'(x)=\frac{(e^{x}-\sec^{2}{x})(\sin{x}+3)-(e^{x}-\tan{x})(\cos{x})}{(\sin{x}+3)^{2}}\]Should I keep going or is this good?

Answer 4

Mmm looks good so far :)

Answer 5

Are you asking whether or not you should simplify further?

Answer 6

Yes @zepdrix

Answer 7

Looks good where it is.
Just depends on what your teacher expects I guess..

Answer 8

that's the quotient rule, not logarithmic diff

are you sure you weren't supposed to take logs first?

Answer 9

Well... is it \(possible\) to simplify further?

Oops, sorry, I meant "Derivatives of Trigonometric Functions," my bad. @IrishBoy123

Answer 10

it doesn't really simplify anymore tho..

Answer 11

You could expand out all the brackets and some of the trig stuff would change .. I don't think there will be any like-terms to combine though.

So it would end up looking "different",
not necessarily "simpler" though.

Answer 12

Alright, then. That works.
Thank you @zepdrix :-)

Answer 13

np kittimittens D: buhaha

Answer 14

I am not a mitten D:< ! lol

Answer 15

i call my kitty mr mittens c: had to try it on you lol

Answer 16

He thinks he's so fancy in his furry tuxedo c:

Answer 17

lol :3

Answer 18

Send pix pls

Answer 19

Lol

Answer 20

@kittiwitti1 This isn't mr mittens, I don't have a picture of him :P

This is his fat friend though.
I caught a funny picture of him taking a nap the other day lolol

Answer 21

@kittiwitti1 XD lol

Answer 22

THAT IS ADORABLE. @zepdrix