implicit differentiation; Find the slope of the tangent line

[killasnake]

I need help with this question. How would I used the implicit differentiation to find the tangent line?

Use implicit differentiation to find the slope of the tangent line to the curve

_Y ____= x^4 -3
x- 9y

 

[stapel]

_Y ____= x^4 -3
x- 9y

I'm sorry, but I can't figure out what this might mean.

Are "Y" and "y" two different variables, so this equation actually has three variables? Or, contrary to standard practice, do you mean "Y" and "y" to be the same?

Are you supposed to find the tangent to some particular point? Or are you just supposed to find the equation of the derivative?

Is the equation "Y/(x - 9y) = x⁴ - 3", or something else?

When you ask how to use implicit differentiation, do you mean that this hasn't been covered in class yet, and you're needing a lesson?

When you reply, please show all of your work, even if you think it is wrong. Thank you.

Eliz.

 

[galactus]

Is this it:

\(\displaystyle \L\\\frac{y}{x-9y}=x^{4}-3\)?.

Implicit differentiation is the same as 'regular' explicit differentiation, except you stick a dy/dx next to the y's when you differentiate, then solve for dy/dx.


Quotient rule for the left side:

\(\displaystyle \L\\\frac{(x-9y)\frac{dy}{dx}-[y(1-9\frac{dy}{dx})]}{(x-9y)^{2}}=4x^{3}\)

Now, finish up?.

 

[killasnake]

sorry I might that to be a lower case y typing the whole equation down takes time and I didn't realize the mistake. By the way how do you guys right out the equation as a gif file? Is their a program?

and yes I can finish the problem now thank you for the help.

 

[galactus]

That's not a gif file, it's a mathematics code called LaTex. I merely type it out manually. Click on 'quote' at the upper right corner of my post to see the code I used. It takes a little practice at first, but it's easy once you get use to it.

You can download software called TexAide, but I think it's just as easy to type it out as use that.