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.