Question

can somebody PLEASE HELP ME./ its urgent/
Use implicit differentiation to find an equation of the tangent line to the graph at the given point.
x + y − 1 = ln(x4 + y13), (1, 0)

Answer 1

first step is to differntiate both sides of the equation

Answer 2

so the left side I would just get 1 ?

Answer 3

but i cant if i have two different variables

Answer 4

no youcan when you do implicit differentiation.. you can do it... so differentiate (d/dy) the whole problem

Answer 5

when you do it, for every y term you'll get a dy/dx

Answer 6

so for hte left side, i would just be left with dy/dx? because the x and the 1 will go away ?

Answer 7

you have to employ the chain rule when dealing with y

Answer 8

Is the argument of the log 4*x+13*y or is it x^4+y^13?

Answer 9

I solved the problem using the first, but I'll redo the solution if necessary.

Answer 10

THIS IS HOW the probelem looks like sorry for the caps x + y − 1 = ln(x4 + y13),

Answer 11

can you please try to solve it the way o psoted? I uregently need help and would relaly appreciate it

Answer 12

If the argument of the log is (4x+13y), then the slope is -8/9, and the method is:
1+y'=(4+13y')/(4x+13y)
(4x+13y)(1+y')=4+13y'
4x+4xy'+13y+13yy'=4+13y'
4xy'+13yy'-13y'=4-13y+4x
y'(4x+13y-13)=4x-13y+4
y'=(4x-13y+4)/(4x+13y-13)
y'(x=1,y=0)=(4-0+4)/(4+0-13)=-8/9
Note: if the 4 and the 13 in the argument of the log are exponents, then obviously this is not the correct solution.

Answer 13

oh shoot. sorry its x^4 and y ^ 13.

Answer 14

lol

Answer 15

I'm lol too Lagrange!

Answer 16

Obsolete, give me a few minutes to adjust the derivative on the RHS.

Answer 17

Disclaimer: I did this pretty quickly.
1+y'=(4x^3+13y^12y')
Clear denominators and multiply on the LHS to get
x^4+x^4y'+y^13 +y13y'=4x^3+13y^12y'
Collect y' terms and factor out
y'(x^4+y^13-13y^12)=4x^3-x^4-y^13
y'=(4x^3-x^4-y^13)/(x^4+y^13-13^12)
y'(x=1,y=0)=(4-1-0)/(1+0-0)=3 which is the slope at (1,0)

Answer 18

Note: I dropped the y-variable in the last term in the second to last line.
-13^12) should read -13y^12)