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
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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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
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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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0402abdb-7df9-4be8-b8f0-4c869f0de12a%2F5b69e308-9b24-4147-8c71-c47659f9ab08%2F3vzgcev_processed.png&w=3840&q=75)
Transcribed Image Text:Jupyterhub Lab 8 (1) Last Checkpoint: 3 minutes ago (unsaved changes)
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View
Insert
Cell
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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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