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Home > CALC > Chapter 8 > Lesson 8.2.1 > Problem 8-67

8-67.

Find $\frac { d y } { d x }$ for the following functions. Then evaluate the derivative at the given point.

$\frac { 2 } { x } - \frac { 1 } { y }= 1$ ; $(1,1)$
Step 1(a):
$-2x^{-2}+y^{-2}y^\prime=0$
Step 2(a):
$-2(1)^{-2}+(1)^{-2}y^\prime=0$
Now solve for $y^\prime$ .

$x^2y − y^3 = 8$ ; $(−3, 1)$
Step (b):
$2xy+x^2y^\prime-3y^2y^\prime=0$

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