= 0.
Next, because = 1, we can eliminate that term and we can distribute the −16 to get 2x − 16x
− 16y + 2y = 0.
Next, group the terms containing on one side of the equals sign and the other terms on the
other side: −16x + 2y = 16y − 2x.
Factor out the term (2y − 16x) = 16y − 2x. Now we can isolate ,
which can be reduced to .
3.
First, cross-multiply so that we don’t have to use the Quotient Rule: x + y = 3x − 3y. Next,
simplify 4y = 2x, which reduces to y = x. Now, we can take the derivative: = . Note that
just because a problem has the x’s and y’s mixed together doesn’t mean that we need to use
implicit differentiation to solve it!
4.
We take the derivative of each term with respect to x: (32x) − 16 +
= 0.
Next, because = 1, we can eliminate that term to get 32x − 16x − 16y + 2y = 0.
Next, don’t simplify. Plug in (1, 1) for x and y: 32(1) − 16(1) − 16(1) + 2(1) = 0,
which simplifies to 16 − 14 = 0.
Finally, we can solve for .
