Slope of the tangent line to x∛y +y∛x = 10 at (1,8).

[Theo_1995]

Hello! So as the title indicates, the full question is as follows:
1. Find the slope of the tangent line to x∛y +y∛x = 10 at (1,8).

I'm getting thrown off by the use of x and y in the same terms. Can someone help me out here? Thanks!

Edit: Read the guidelines and no, I don't have any thoughts about this one because oddly, it's the only one I don't know where to begin with tbh... I've already reached anti-derivatives tho and was able to answer them. I think I just don't get the gist of what to do honestly with this one : ))

 

[BigBeachBanana]

Hello! So as the title indicates, the full question is as follows:
1. Find the slope of the tangent line to x∛y +y∛x = 10 at (1,8).

I'm getting thrown off by the use of x and y in the same terms. Can someone help me out here? Thanks!

Edit: Read the guidelines and no, I don't have any thoughts about this one because oddly, it's the only one I don't know where to begin with tbh... I've already reached anti-derivatives tho and was able to answer them. I think I just don't get the gist of what to do honestly with this one : ))

Implicit differentiation to find the slope.

 

[Steven G]

Use product rule.

 

[Theo_1995]

Hello! Just got back. Would the answer be -56/13?

 

[BigBeachBanana]

Hello! Just got back. Would the answer be -56/13?
View attachment 32514

Yes, that's correct. Now you can finish finding the tangent line.

 

[Theo_1995]

Huh? There's still more steps to this?

 

[BigBeachBanana]

Huh? There's still more steps to this?

My mistake, I thought the question asked for the tangent line, and not just the slope.

 

[Theo_1995]

Oh okie. Thank you guys so much!