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# (a) Find $y'$ by implicit differentiation.(b) Solve the equation explicitly for y and differentiate to get $y'$ in terms of $x.$(c) Check that your solutions to part (a) and (b) are consistent by substituting the expression for $y$ into your solution for part (a).$2x^2 + x + xy = 1$

## a. $\frac{-(4 x+1+y)}{x}$b. $\frac{-2 x^{2}-1}{x^{2}}$c. See explanation

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

in this problem, we're gonna function to expert was exposed Father Zico One in part A whereas to find Garrett. Why? Using sex appreciation. So let's take their it off. All the terms of suspect X. We have four eggs or sport transported for turn. We're going to use a product rule. So we have Why Waas It's time there. Why? Which is divine X, and that is a zero since one majestic constant. So from this we see that the little boy you find Jens he could do negative off or x plus y los form divided by X How important we were as two point explicitly friend punching y and detector that we see that except for is a good one minus two expert. But it's so promise. We see that boy's anything for money to experience. What X you mind by s all right. No, let's take their toll dysfunction. Um, actually, it's percent dysfunction. This one over X minus two experts. Well, now let's take them Talk. This this gives us why point as negative or or expert? Minus, um two. So that is then negative. Off to ex script was one divided by X squared warrant. Now let's take very talk to function that the phone for a which is negative off four X plus y plus one divine by ex Now in party we fell. What? What s So let's just put that in. That is a negative off four x plus y where why is seeking to, um plus war waas One of X months to x um, mice form the soul thing divided by eggs. Negative or positive. One cast out. Go have negative off to Lex was born over x divine, but next and that is equal to negative. Off to expert wasp born give I extract. As you can see, this is same as the decorative return be so implicit and explicit differentiation gives us the same results.

#### Topics

Derivatives

Differentiation

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp