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Find the derivatives of the given functions.$$y=\log _{7}\left(x^{2}+4\right)$$

$\frac{d y}{d x}=\frac{2 x \log _{7} e}{x^{2}+4}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 5

Derivative of the Logarithmic Function

Derivatives

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Yeah, we want to find the derivative dy dx for why is equal to log seven of X squared plus four. To do so we're going to be relying on differentiation shortcuts. We picked up that single edible kelp related to transcendental functions in particular those related to longer ethnic functions that we've recently learned. So I've listed relevant rules for derivative taking here on the left. Rule zero is the rules for derivative, a lobby of you and the natural algorithm end of you. We also have on the right powerful product rule in chain will respectively. And this problem will need to rely on D D X log bu and World Zero, which implicitly involves a chain role to solve. So Y equals log seven X squared plus four variants. Most easily defensible for that means you can proceed to solve. We have do idea is one over X squared plus four. One over you. Times log 70 log B e times two X. Which is the U D X. Simplifying. We have do I d x equals two x over x squared plus four Times Log seven of E.

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