Question

Find an equation of the tangent line to the graph of the equation at the given point.

arctan (x+y)=y^2 + pi/4 point: (1,0)

Work so far attached, I'm stuck.

Answer 1

are you working in this?

Answer 2

You mean the OS Equation Editor? No

Answer 3

i meant the first equation

Answer 4

I have to go to bed so feel free to input anything that will help me solve the problem and I'll check this question in the morning

Answer 5

i think it is fast

Answer 6

well yes, my work is attached

Answer 7

can you wait some minutes?

Answer 8

Okay, sure

Answer 9

only the first equation , right?

Answer 10

there's only one equation, so yes

Answer 11

Yes, the formula is u'/(1+u)^2

Answer 12

Yes... I did that but what confused me was that I had y' on both sides

Answer 13

wait

Answer 14

y' is the slope of the tangent

Answer 15

at point (1,0)

Answer 16

it means to evaluate it for x=1 and y=0

Answer 17

but you need y' on one side to get the slope of the tangent, right?

Answer 18

wait me 3 minuts please

Answer 19

plug in the numbers then solve it is easier

Answer 20

But I need to find the actual derivative before I can solve and that's what's tripping me up

Answer 21

oh i see ok
\[\tan^{-1}(x+y)=y^2\] to start, then
\[\frac{y'+1}{(x+y)^2+1}=2yy'\]

Answer 22

right so since the y' is on both sides what do I do

Answer 23

factor it out right

Answer 24

replace it for the point that you want

Answer 25

you have a choice
ugly algebra, or plug in the numbers now

Answer 26

Okay... so numbers

Answer 27

i would choose the second one because it is much much easier

Answer 28

so what I just plug in for x and y?

Answer 29

replace \(x\) by 1, \(y\) by 0

Answer 30

point: (1,0)

Answer 31

so then ?

Answer 32

\(\frac{y'+1}{2}=0\) you can just about solve for \(y'\) in your head

Answer 33

so my work is correct?

Answer 34

slope is \(-1\) right? then i guess point - slope to get the line

Answer 35

Yeah I did all that and got y=-x+1

Answer 36

yeah, looks good

Answer 37

Okay cool, thanks man