Question

Use implicit differentiation to find an equation of the tangent line to the graph at the given point.
x + y − 1 = ln(x^4 + y^13), (1, 0)

Answer 1

satellite this one:S

Answer 2

you come up with the doozies

Answer 3

take the derivative wrt x and get
\[1+y'=\frac{1}{x^4+y^{13}}\times (4x^3+13y^{12}y')\]

Answer 4

can someone please help me

Answer 5

now solve this for y' but since all you really need is the derivative when x = 1 and y = 0, just replace x by 1 and y by 0 in that equation and solve for y'

Answer 6

sorry my comp froze ehnc ei asked for help again

Answer 7

\[1+y'=1\times 4\]

Answer 8

\[y'=3\]

Answer 9

so it looked bad but substitution made it simple

Answer 10

hope it is clear, gotta run

Answer 11

wait so y=3 is the equation?

Answer 12

?

Answer 13

The slope of the tangent would be 3. So the tangent line is:\[y-0=3(x-1)\]Giving:\[y=3x-3\]