# dy/dx

• September 26th 2009, 01:20 PM
Nightasylum
dy/dx
and evaluate the derivative at the given point.

x^(2/3) + y^(2/3)=5 (8,1)
• September 26th 2009, 01:30 PM
e^(i*pi)
Quote:

Originally Posted by Nightasylum
and evaluate the derivative at the given point.

x^(2/3) + y^(2/3)=5 (8,1)

$y^{\frac{2}{3}} = 5 - x^{\frac{2}{3}}$

$y = (5-x^{\frac{2}{3}})^{\frac{3}{2}}$

By the chain rule:

$\frac{dy}{dx} = \frac{3}{2}(5-x^{\frac{2}{3}})^{\frac{1}{2}} \times -\frac{2}{3}x^{-\frac{1}{3}}$

$
=-\frac{\sqrt{5-x^{\frac{2}{3}}}}{\sqrt[3]{x}}$

$f'(8) =-\frac{\sqrt{5-8^{\frac{2}{3}}}}{\sqrt[3]{8}} = -\frac{1}{2}$
• September 26th 2009, 01:39 PM
Nightasylum
yu sure it wouldnt be - 1/2?
• September 26th 2009, 01:50 PM
e^(i*pi)
Quote:

Originally Posted by Nightasylum
yu sure it wouldnt be - 1/2?

You're right, it should be -1/2. For whatever reason I didn't see that minus sign >.<

Edited in the above post now