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Find the derivatives of the given functions.$$y=x-\ln ^{2}(x+y)$$

$\frac{d y}{d x}=\frac{x+y-2 \ln (x+y)}{x+y+2 \ln (x+y)}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 5

Derivative of the Logarithmic Function

Derivatives

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uh huh. We want to find do I dx derivative for the function Why is equal to x minus natural algorithms squared of X plus Y. We need to use derivatives shortcuts for transcendental functions, which is a natural algorithms to solve. So I've noted the relevant rules here, rules here on the left is dD extra log Bu and Ellen you on the right. And to the power rule products will in general, respectively. And this role will need both Rule zero and roll three. Rule three is especially important because why on both sides of this equation and therefore we need to invoke implicit differentiation. So implicit differentiation gives us DDX of both sides is equal. Therefore we have D I D X. For the channel is equal to one by the power rule minus two. L N X plus Y. Times for the chain rule one over X plus Y times one plus dy dx. We want to solve this expression for dy dx. So if we isolate dy dx terms, we obtain solution X plus Y minus two, X plus Y over X plus Y plus two, L n x plus Y as his box at the bottom.

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