Mathematics, 15.07.2019 15:30 Porciabeauty4175
Find y'' by implicit differentiation. 3x^3 + 4y^3 = 5
Answers: 1
so 
 and 
. That's the first derivative. Now for the second it's probably easiest to use the quotient rule, even though it's usually long and drawn out. That looks like this: ![\frac{dy}{dx}= \frac{4y^2(-6x)-[-3x^2(8y \frac{dy}{dx})] }{(4y^2)^2}](/tpl/images/0092/9689/484b1.png)
 which simplifies a bit to 
. We will multiply both sides by that denominator to get rid of it which leaves us with 
. Get both dy/dx terms on the same side, and then factor it out. 
. Divide to isolate the dy/dx: 
. There's no simplifying you could do after that that would make any significant difference.
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Find y'' by implicit differentiation. 3x^3 + 4y^3 = 5...
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