Exercise Question 1. Find for √y²+x²-6y 3xy = y* using implicit differentiation. x(x)² If you've done it correctly, the result should look like: _—_y(x) = _ 3³√x²+y(x)²x²x(x)*+*² log (x(x))+>(x)³_6√/x²+x(x)² »{x}² - 3√√x²+y(x)²x²³x(x)x+¹+x³ 31

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Exercise Question
1. Find
dy
dx
for
√y²+x²-6y
3xy
=
using implicit differentiation.
If you've done it correctly, the result should look like: y(x)
dx
3√√x²+y(x)² x²y(x)*+² log (v(x))+v(x)³−6√/\x²+v(x)² v(x)²
3√√/x²+y(x)² x³y(x)x+¹+x²
3
Transcribed Image Text:Exercise Question 1. Find dy dx for √y²+x²-6y 3xy = using implicit differentiation. If you've done it correctly, the result should look like: y(x) dx 3√√x²+y(x)² x²y(x)*+² log (v(x))+v(x)³−6√/\x²+v(x)² v(x)² 3√√/x²+y(x)² x³y(x)x+¹+x² 3
Jupyterhub Lab 8 (1) Last Checkpoint: 3 minutes ago (unsaved changes)
File
Edit
View
Insert
Cell
▶ Run
●
Kernel
Widgets Help
Code
MATH1110 Lab 8~ Tangents
In [4]: #remember to include these two lines of code at the start of your document!
from IPython.core.interactiveshell
InteractiveShell.ast_node_interactivity
import InteractiveShell
= "all"
• Define the variable that you will be differentiating with respect to as a variable
• Define the variable that you want the isolated derivative for as a function of the previous variable
Assign (using one =) your two sided equation to be a function with two
== between the sides
• Show the equation to double check you typed it correctly
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2. Review of implicit differentiation
We can find derivatives of a function by plugging it into derivative() or diff(). For implicit differentiation, we have to set up our variables and functions a little
differently. This is the process:
Control Panel
SageMath 9.0 O
• Use solve() to find the derivative of your equation with respect to x, where the second argument is dy, which you want Sage to solve for
Show the final result
• Take the derivative of your function variable (typically y) with respect to the other variable (typically x) and define this to be dy (or whatever your function
variable is called)
Transcribed Image Text:Jupyterhub Lab 8 (1) Last Checkpoint: 3 minutes ago (unsaved changes) File Edit View Insert Cell ▶ Run ● Kernel Widgets Help Code MATH1110 Lab 8~ Tangents In [4]: #remember to include these two lines of code at the start of your document! from IPython.core.interactiveshell InteractiveShell.ast_node_interactivity import InteractiveShell = "all" • Define the variable that you will be differentiating with respect to as a variable • Define the variable that you want the isolated derivative for as a function of the previous variable Assign (using one =) your two sided equation to be a function with two == between the sides • Show the equation to double check you typed it correctly Trusted Logout 2. Review of implicit differentiation We can find derivatives of a function by plugging it into derivative() or diff(). For implicit differentiation, we have to set up our variables and functions a little differently. This is the process: Control Panel SageMath 9.0 O • Use solve() to find the derivative of your equation with respect to x, where the second argument is dy, which you want Sage to solve for Show the final result • Take the derivative of your function variable (typically y) with respect to the other variable (typically x) and define this to be dy (or whatever your function variable is called)
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