Re: Implicit Differentiation

You differentiated correctly, now use the given point (2,-12) to find y'(2). Then use the point-slope formula to find the equation of the tangent line.

Re: Implicit Differentiation

Instead of making a new thread on these, I want to just pop in a quick question to see if I implicitly differentiated this correctly; problem is $\displaystyle (6x-y)^4+3y^3=9976$, and I implicitly differentiated y with respect to x to get this $\displaystyle dy/dx = \frac{(24(6x-y)^3)}{(1+9y^2)}$ ... Does that look about right? I have a gut feeling it isn't, but I've combed through it a few times and I'm not sure how else to differentiate it. Thanks!

Re: Implicit Differentiation

I get a different result...can you post your work?

Re: Implicit Differentiation

Thanks for your help, I think I got it. The slope came out to -11/2 and the equation for the tangent line came out to be y=-11/2(x)-1. Thanks again!!

Re: Implicit Differentiation

Yes, I get the same result. :)

Re: Implicit Differentiation

Quote:

Originally Posted by

**MarkFL2** I get a different result...can you post your work?

Should've posted it originally, my bad. Here it is:

$\displaystyle (6x-y)^4+3y^3=9976$

$\displaystyle d/dx[(6x-y)^4]+d/dx[3y^3]=d/dx[9976]$ (Took derivative with respect to x)

$\displaystyle 4(6x-y)^3*6*(-1)*(-dy/dx)+9y^2*dy/dx=0$

$\displaystyle -24(6x-y)^3*(-dy/dx)+9y^2*dy/dx=0$ (multiplied 6 and -1 by 4)

$\displaystyle dy/dx(24(6x-y)^3+9y^2)=0$ (factored out a dy/dx and got rid of the -1 by multiplying it by -24)

This is where I'm confused, and I have a feeling it's because I'm not doing something right when I differentiated the inside function -y from (6x-y)^4?

Or I should revisit step 4 and divide the left side and right side of the equation by -24.

$\displaystyle \frac{-24(6x-y)^3*(-dy/dx)+9y^2*dy/dx}{-24}=\frac{0}{-24}$

$\displaystyle dy/dx[(6x-y)^3*-1+9y^2]=0$ (now factor out dy/dx)

Actually that's still going to be wrong because dy/dx isn't going to be zero. I must need to add or subtract something from the left to get a quantity on the right?