Answer
Slope = $ -15^{-\frac{3}{4}}$
Work Step by Step
We find:
$x^4+y^4 = 15$
$4x^3 +4y^3 \frac{dy}{dx} =0$
$\frac{dy}{dx} = -\frac{x^3}{y^3}$
$\frac{dy}{dx} |_{(1,15^{\frac{1}{4}})} = -\frac{1^3}{(15^{\frac{3}{4}})} = -15^{-\frac{3}{4}}$
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 2 - The Derivative - 2.7 Implicit Differentiation - Exercises Set 2.7 - Page 166: 27
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