330
Chapter 3 | Derivatives
ln y = ln x r ln y = r ln x
Step 1. Take the natural logarithm of both sides. Step 2. Expand using properties of logarithms.
dy dx = dy dx = dy dx = dy dx =
1 y
r 1 x
Step 3. Differentiate both sides.
y r x
Step 4. Multiply by y on both sides.
x r r x
Step 5. Substitute y = x r .
rx r −1
Simplify.
Use logarithmic differentiation to find the derivative of y = x x .
3.54
Find the derivative of y = (tan x ) π .
3.55
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