warm up problems 1. 2. 3.. after correcting the homework, we will be taking derivative quiz #2
TRANSCRIPT
![Page 1: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/1.jpg)
Warm up Problems
1.
2.
3.
2ln
dx
dx
2 1tand
y ydy
1ln
tde
dt
![Page 2: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/2.jpg)
After correcting the homework, we will be taking Derivative Quiz #2.
![Page 3: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/3.jpg)
![Page 4: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/4.jpg)
Implicit Differentiation
Ex. 5dy
dx
So far, all problems have been y = f (x)
What if x’s and y’s are mixed together?
![Page 5: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/5.jpg)
Ex. If cos x + y2 – y = x, find .
Steps for Implicit Differentiation
• Derivative of x-function is the same as usual.
• Derivative of y-function gets .
• If x’s and y’s mixed, use product rule.
• Solve for .
dy
dx
dy
dx
dy
dx
![Page 6: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/6.jpg)
Ex. If cos x + y2 – y = x, find . dy
dx
![Page 7: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/7.jpg)
Ex. 2 4ln 5xy x y e
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Pract. 2 2 16x y
Pract. 3 3 10x y y
![Page 9: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/9.jpg)
Ex. Find the slope of the line tangent to y = x + cos(xy) at the point where x = 0.
![Page 10: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/10.jpg)
Ex. If cos x + y2 – y = x, find . 2
2
d y
dx
![Page 11: Warm up Problems 1. 2. 3.. After correcting the homework, we will be taking Derivative Quiz #2](https://reader031.vdocument.in/reader031/viewer/2022020723/551451005503462d4e8b50f3/html5/thumbnails/11.jpg)
Ex. Find the coordinates of any point on x2 + y2 = 16 where the tangent line has
the slope of -1.