Question

y /((x-(-6)) = x^8 + (-7)
Use implicit differentiation to find the slope of the tangent line to the curve at point (1, -6/37)

Answer 1

Do you know how implicit differentiation works?

Also, is the following your equation (just for clarity):

\[\frac{y}{x + 6} = x^8 - 7\]

Answer 2

how did you do that??

Answer 3

If you press the equation button below a reply you can use formatting. It doesn't work when posting a question; for that reason, if you're posting a complicated equation (probably not necessary in this case) I find it's best to post it in the comments.

Answer 4

ah ok thanks

Answer 5

In reference to the question, it would be good to know this:
What do you know about implicit differentiation at this point? Do you know how to start the problem using it?

Answer 6

yes
well I know that if I diff. \[x ^{8}+7 \] I will get \[8x ^{7}\]

Answer 7

It seems like you're not actually especially used to implicit differentiation. Essentially, implicit differentiation is differentiating an entire equation with respect to a variable, in this case x. To get started, I suggest you multiply throughout by x+6 and simplify the right hand side; this should make the calculus essentially trivial.

Answer 8

\[(x ^{8}-7)(x+6)\]

Answer 9

Yup. Expand that out, then differentiate the equation (including the left side) with respect to x.

Answer 10

\[y'=8x^{7}\]

Answer 11

?

Answer 12

Uhm, you seem to have dropped a couple of terms completely!

\[(x^8 - 7)(x + 6) = x^9 + 6x^8 - 7x - 42\]

Answer 13

oh you factored

Answer 14

that would be \[9^{8}+48x ^{7}-7\]

Answer 15

\[9x ^{8}\]

Answer 16

Yup.