Asked by Maddie
How do I find the derivative of e^y -y=x^2 -2?
Do I use chain rule with -d/dy or -d/dx or dy/dx?
And then how do I find the slope of the graph if the point's at (2,0)?
Do I use chain rule with -d/dy or -d/dx or dy/dx?
And then how do I find the slope of the graph if the point's at (2,0)?
Answers
Answered by
Reiny
Use implicit differentiation.
e^y -y=x^2 -2
e^y (dy/dx) - dy/dx = 2x
dy/dx( e^y - 1) = 2x
dy/dx = 2x/(e^y -1)
so for the point (2,0), dy/dx = 2(2) / (e^0 - 1)
= 4/0
this tells me that at (2,0) the tangent slope is undefined, thus the tangent will be a vertical line
The equation will be x = 2
e^y -y=x^2 -2
e^y (dy/dx) - dy/dx = 2x
dy/dx( e^y - 1) = 2x
dy/dx = 2x/(e^y -1)
so for the point (2,0), dy/dx = 2(2) / (e^0 - 1)
= 4/0
this tells me that at (2,0) the tangent slope is undefined, thus the tangent will be a vertical line
The equation will be x = 2
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.