Question

Implicit differentiation to find the slope of the tangent line

Answer 1

\[\frac{ y }{ x-3y }=x^9-2\]
differentiate w.r.t. x
\[\frac{ \left( x-3y \right)\frac{ dy }{ dx }-y \left( 1-3 \frac{ dy }{ dx } \right) }{ \left( x-3y \right) ^2}=9x^8\]
\[\left( x-3y+3y \right)\frac{ dy }{ dx }-y=9x^2\left( x-3y \right)^2\]
\[\frac{ dy }{ dx }=9x \left( x-3y \right)^2\]
put x=1,\[y=\frac{ -1 }{ -2 }=\frac{ 1 }{ 2 },we~get\]
?

Answer 2

so do i plug in the x and y into the 9x(x-3y)^2 ?

Answer 3

it gave me 2.25

Answer 4

correction it is\[9 x^7(x-3y)^2\]
i wrote by mistake 9x^2,it should be 9x^8

Answer 5

in place of 9x write 9x^7

Answer 6

it would still give the same answer since x is 1 isn't it?

Answer 7

but the answer remains the same.

Answer 8

it says the answer is incorrect?

Answer 9

i feel like im doing something wrong but im not sure

Answer 10

you can use the quotient rule, or you can multiply out first

Answer 11

might be easier to do with with
\[y=(x^9-2)(x-3y)\] i.e.
\[y=x^{10}-3 x^9 y-2 x+6 y\]

Answer 12

then do i find the derivative of that?

Answer 13

wait that confuses me

Answer 14

yes differentiate that