#Implicit Differentiation Calculus 2.5

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south lintel
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Help 27, 32, 34

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uneven stratusBOT
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south lintel
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I have tried product rule, quotient rule, chain rule and etc but I can’t figure these problems out they’re too hard

south lintel
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Anyone available

pseudo raft
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isolate y

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say for xy=6
divide both sides by x

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the you get y=6/x

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then

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dy/dx = -6/x^2

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for 28, divide both sides by 3x^3

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for 29, square root both sides

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for 32, arctan and then subtract x

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basically, just isolate y

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I'll do 33 for a better example

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$3e^{xy} - x = 0$

$3e^{xy} = x$

$e^{xy} = \frac{x}{3}$

$xy = \ln{(x)} - \ln{(3)}$

$y =\frac{\ln{(x)} - \ln{(3)}}{x}$

$\frac{dy}{dx} = \frac{1 - \ln{(x)} + \ln{(3)}}{x^2}$