Lesson 6 Nov 23 24 09
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Transcript of Lesson 6 Nov 23 24 09
Implicit Differentiation
y = 5x + 1Derivative?
Explicit differentiation
Having the dependent variable expressed directly in terms of the independent variable.
Given y2 2x = y
Find y '
Step 1. Take derivative of each sideddx( )y2 2x = d
dx( )y
dydx= 22y 1
Step 2. Put all terms with on the same sidedydx
Step 3. Factor out dydx
Step 4. Solve for dydx
y2 2x = y
Find the slope of the tangent line at (1, 1)
if x2 + y2 = 36Find dydx
xy
Find dydx if 2x3 3y3 = 4xy
Product Rule
ddx[ f(x) g(x). ] = f '(x).g(x)f(x) . g '(x) +
Find dydx x y8 + 6x = 3y
4y + xy6xy3 4x
Find dydx
cos y + x3 = sin x
3x2 cos xsin y
3e5x + 6ey2 = 8Find dy
dx5e5x
4yey2
What is the slope of the tangent line to
5x2 +3xy + 2y2 + 12y 5 = 0
at the point (1, 0)
exercise 4.5
Questions 1 23