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Find the derivatives of the given functions.$$y=0.6 \ln \left(e^{5 x}+3^{4}\right)$$

$\frac{d y}{d x}=\frac{3 e^{5 x}}{c^{5 x}+3^{4}}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 6

Derivative of the Exponential Function

Derivatives

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Uh huh. We want to find dy dx the derivative of Y. With respect to X. For the function Y equals 0.6. Alan E. V. Five X plus 3/4. So just all we're gonna rely on different events shortcuts namely we're gonna rely on rule 0 to 3 here. Zero. Malek is D D X. B T. U equals B. To the L N B. D. U D X. D X. E D. U. Is E D U D U. D. X. Rules one through three of the power rule. Product rule in general, respectively. Will have to rely On the power rule chain. Roll in. Roll 0 to solve so why equals 0.6 led the five exposed three to the fourth has already written and the easiest form differentiate so we can proceed right to solving. Dy dx is 8.6. Either five X times five over either five actual three. The fourth this is using the natural longer than derivative which is D D X. L N X is one over X or D D. Excel in You is d u d x overview. That's your final solution. DY DX is equal to three E 25 X, divided by either the five X plus 81.

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