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Question

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

Tyler Moulton · Accepted Answer

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&#x27;re gonna rely on different events shortcuts namely we&#x27;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&#x27;s your final solution. DY DX is equal to three E 25 X, divided by either the five X plus 81.

Jessica Wellington · Answer

it is four point four. Number six. Why equals negative for E to the negative point three x So we&#x27;re looking for the derivative. So do I. D Eggs is equal to the original function going for E you&#x27;re four. To recreate that negative for E to the negative point three x times the derivative of what I have written and read, which is negative. Point three. We simplify this. The negatives cancel and you get one point two to the negative point three x as your final answer again. Any time you&#x27;re differentiating an exponential function with Annie, it&#x27;s the function times the derivative of what&#x27;s in the X.

Linh Vu · Answer

but the function Why ICO to Manus Far age Moniz upon Tree X and the question asked to find a y prime and reconnect every under each of the function of the banks, the river tive And then we should get agent a huge of the X times the your prem on the axe and usually this form that we can identify. The power here will be the year off X and they found a weapon. A coach You from the constant are in the front here we will be staying the same and then times with each other. Berman is the country x on by the formula we need to multiply and pine it upon three x derivative Now the Minnesota Country X derivative Heico German and Serpent three minus urban three times with the Manus far go to one point you aged repairman is the country X on This will be the UAE prime that we&#x27;re looking for

Robert Daugherty · Answer

problem number 27 Section 45 Again, Everything in this section deals with finding derivatives of functions that involve logarithms. So here I have. Why is equal to e to the five X divided by the natural log of three x each of the five x over the natural log of three to the X. So again, guiding principle here I&#x27;ve got something that looks like y is equal to F over G. Why prime is quotient rule F prime G minus G prime f over cheese squared. In my particular case, eat of the five x represents F and natural law. Go three x represents a g. So to go find this derivative. So why Prime is going to be equal to F Prime G. So the derivative eat of the five X is five e to the five X so that&#x27;s F primes, Then times G. That&#x27;s gonna be times natural Log of three x minus G prime f So g prime f. That is gonna be what one over three x times 32 That&#x27;s G prime. All of that times F, which is either the five x over G squared, which is Ellen of three x squared and it looks like I can simplify a bit by multiplying everything by five X. And so I multiply everything by five acts she meet motive, everything by X because what you&#x27;re going to see here? I&#x27;ve got three over three I can keep from having a complex fraction if I multiply everything so by X so I&#x27;m gonna have five x e to the five x natural log of three X and then minus E to the five x over X natural log of three X and then all of that is squared and it looks like I could probably factor out and eat to the five X, um, for a further simplification. So if I were to do that, I&#x27;m gonna have e to the five X and then I&#x27;m left with five x natural log of three X minus one, all of that divided by X natural log of three x squared. So each of the five x five x of natural log of three X minus one over X natural log of three x All that quantity squared

Jessica Wellington · Answer

here we have four point four. Number ten were asked to find the derivative of this function. We have an exponential here. So the derivative of an exponential function is the entire function which is negative fiv e to the four x cubed times the derivative of what I have written and read. So we&#x27;re taking We&#x27;re just looking at the derivative, that part right here, which is twelve x squared. And we can simplify this too. Negative sixty that twelve times negative five X squared game to the four ex cute for our final

Linh Vu · Answer

But why? Ego Ju minus five times aged about off expound three on the question asked to find a y prime recorded, It would have the exponential under function on the X the river to which you get in Cultural agent, The new off extends your print off X. And now when you this formula here we can identify the power here We&#x27;ve been your x f or by formula. First, the constant here will stay the same temps teaching for X poetry terms with the for expert really riveting off and now under far eggs Valentini Really day we called you, but a blind power rule here which you get a drought X crap temps with them. Honest five attempts. Agent of far expert tree Here we can win. Tonight is with drill. Therefore, we got it got u minus 60. We can grow in the X ray to the front, aged about four x poetry. And this will be the white Bram. Then we&#x27;re looking from here

Problem

Find the derivatives of the given functions. $$R=…

Problem 8 Easy Difficulty

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

Answer

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

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

Basic Technical Mathematics with Calculus

Catherine R.

Caleb E.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Catherine R.

Caleb E.

Samuel H.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus