Question

hey how do i find dy/dx of tan(X+y)=4x?

Answer 1

calc 1 ?

Answer 2

yep

Answer 3

alright and have you learned implicit differentiation

Answer 4

yea im ok with it

Answer 5

i wud subtrac 4x first right?

Answer 6

um not necessarily you can just simply take the dy/dx of both sides right now if you wanted to

Answer 7

oh ,well ill subtract since our teach showed us that n hell b grading it lol

Answer 8

alright now differentiate with the respects to x

Answer 9

dy/dx is respect to x or y?

Answer 10

nvm that, what do i do with the tan(x+y) ?

Answer 11

is it sec^2(x+Y)?

Answer 12

nvm that, what do i do with the tan(x+y) ?

Answer 13

use the chain rule which would be sec^2(u)(u')

Answer 14

deriv of y =1 right?

Answer 15

k so got sec^2(x+y)=4 now

Answer 16

\[\frac{d}{dx}[y]=\frac{dy}{dx}\]

Answer 17

in respects to x... you can't find the derivative of y since it's not x

Answer 18

ok

Answer 19

so you should get

\[\sec^2(x+y)(1+\frac{dy}{dx})=4\]

Answer 20

ahh ok

Answer 21

alright so what do you get for an answer

Answer 22

one sec so now i factor out dy /dx but what happens to sec?

Answer 23

oh wait is answer 4/sec^2(X+y)?

Answer 24

multiply the two to get

\[\sec^2(x+y)+\frac{dy}{dx}\sec^2(x+y)\]

- sec^2(x+y and divide by sec^2(x+y)

\[\frac{dy}{dx}=\frac{4-\sec^2(x+y)}{\sec^2(x+y)}\]

Answer 25

thanks so much