Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.8 Implicit Differentiation - 3.8 Exercises - Page 200: 7


$(a)$. $$\frac{dy}{dx}=\frac{2}{y}$$ $(b)$. SLope of the tangent to the curve is $m=1$

Work Step by Step

$(a)$. Use implicit differentiation to find $\frac{dy}{dx}$ for $y^2=4x$ Taking the derivative implicitly we get: $$2y\frac{dy}{dx}=4$$ Solve for $\frac{dy}{dx}$ $$\frac{dy}{dx}=\frac{4}{2y}=\frac{2}{y}$$ $(b)$. Finding slope of tangent line at the point $(1,2)$ for the above function. We do this by plugging in the point $(1,2)$ into the derivative from part $(a)$. Hence: $$\frac{dy}{dx}=\frac{2}{(2)}=1$$
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