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Warm up Problems
1.
2.
3.
2ln
dx
dx
2 1tand
y ydy
1ln
tde
dt
After correcting the homework, we will be taking Derivative Quiz #2.
Implicit Differentiation
Ex. 5dy
dx
So far, all problems have been y = f (x)
What if x’s and y’s are mixed together?
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
Ex. If cos x + y2 – y = x, find . dy
dx
Ex. 2 4ln 5xy x y e
Pract. 2 2 16x y
Pract. 3 3 10x y y
Ex. Find the slope of the line tangent to y = x + cos(xy) at the point where x = 0.
Ex. If cos x + y2 – y = x, find . 2
2
d y
dx
Ex. Find the coordinates of any point on x2 + y2 = 16 where the tangent line has
the slope of -1.