4x^3 + ln y^2 + 2y = 2x I don't know what those last 3 terms become after differentiating. The first is 12x^2, but what do those 3 become?
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Originally Posted by Archduke01 4x^3 + ln y^2 + 2y = 2x I don't know what those last 3 terms become after differentiating. The first is 12x^2, but what do those 3 become? It is implied that y is a function of x, Therefore, we treat y as composite (composed with x). Do you see my point?
Originally Posted by VonNemo19 It is implied that y is a function of x, Therefore, we treat y as composite (composed with x). Do you see my point? Just to verify that I got your explanation, would that mean the derivatives are; ? I'm messing up somewhere in the calculations. I can't seem to get y(1 - 6x^2) / 1 + y which is the given answer.
Originally Posted by Archduke01 Just to verify that I got your explanation, would that mean the derivatives are; ? I'm messing up somewhere in the calculations. I can't seem to get y(1 - 6x^2) / 1 + y which is the given answer. Everythin looks good except the third term on the left hand side. Should be... not
12x^2 + 2 y'/y + 2y' = 2 2 y'/y + 2y' = 2 - 12x^2 2y' (1/y + 1) = 2 - 12x^2 y' (1/y + 1)= 1 - 6x^2 y' = (1 - 6x^2) / (y + 1) Where did I go wrong? The numerator's supposed to have a y in it, but my answer doesn't yield such a thing.
Originally Posted by Archduke01 12x^2 + 2 y'/y + 2y' = 2 2 y'/y + 2y' = 2 - 12x^2 2y' (1/y + 1) = 2 - 12x^2 y' (1/y + 1)= 1 - 6x^2 y' = (1 - 6x^2) / (1/y + 1) multiply numerator and denominator by y ... y' = y(1 - 6x^2)/(1 + y) Where did I go wrong? The numerator's supposed to have a y in it, but my answer doesn't yield such a thing. ...
Originally Posted by Archduke01 12x^2 + 2 y'/y + 2y' = 2 2 y'/y + 2y' = 2 - 12x^2 2y' (1/y + 1) = 2 - 12x^2 y' (1/y + 1)= 1 - 6x^2 y' = (1 - 6x^2) / (y + 1) Where did I go wrong? The numerator's supposed to have a y in it, but my answer doesn't yield such a thing.
Originally Posted by Archduke01 4x^3 + ln y^2 + 2y = 2x I don't know what those last 3 terms become after differentiating. The first is 12x^2, but what do those 3 become? . . You could clean this up more if you wanted.
Thanks brosephs, I get it now. Damn, that 2 layered denominator was confusing.
Originally Posted by Archduke01 But if we're seeing y as a function, shouldn't we have to apply the chain rule? Sure! That's what we did!
Originally Posted by VonNemo19 Sure! That's what we did! XD yeah I realized that just after I posted. My badness.
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