Calculus Volume 1

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

This OpenStax book is available for free at http://cnx.org/content/col11964/1.12

Made with FlippingBook - professional solution for displaying marketing and sales documents online