For ycos5x + y^2 = 6xlny, Use implicit differentiation to find dy/dx​

1 answer
Question:

for ycos5x + y^2 = 6xlny, Use implicit differentiation to find dy/dx​

Answers

Using implicit differentiation, it is found that:[tex]\frac{dy}{dx} = \frac{5y^2\sin{5x}+6y\ln{y}}{y\cos{5x}+2y^2+6x}[/tex]The function is:[tex]y\cos{5x} + y^2 = 6x\ln{y}[/tex]In implicit differentiation:We apply the standard derivative rules.The numerator is the variable we derived.The denominator is fixed.Applying implicit differentiation:[tex]\cos{5x}\frac{dy}{dx} - 5y\sin{5x}\frac{dx}{dx} + 2y\frac{dy}{dx} = 6\ln{y}\frac{dx}{dx} + \frac{6x}{y}\frac{dy}{dx}[/tex][tex]\cos{5x}\frac{dy}{dx} + 2y\frac{dy}{dx} + \frac{6x}{y}\frac{dy}{dx} = 5y\sin{5x} + 6\ln{y}[/tex][tex]\frac{dy}{dx}(\cos{5x} + 2y + \frac{6x}{y}) = 5y\sin{5x} + 6\ln{y}[/tex][tex]\frac{dy}{dx}\left(\frac{y\cos{5x}+2y^2+6x}{y}\right) = 5y\sin{5x} + 6\ln{y}[/tex][tex]\frac{dy}{dx} = \frac{5y^2\sin{5x}+6y\ln{y}}{y\cos{5x}+2y^2+6x}[/tex]A similar problem is given at https://brainly.com/question/9543179

Similar Solved Questions

1 answer

A closed system of mass 3 kg undergoes a process in which there is a heat transfer of 150 kJ from the system to the surroundings. The work done on the system is 75 kJ. If the initial specific internal energy of the system is 450 kJ/kg, what is the final specific internal energy, in kJ/kg? Neglect changes in kinetic and potential energy. ​

A closed system of mass 3 kg undergoes a process in which there is a heat transfer of 150 kJ from the system to the surroundings. The work done on the system is 75 kJ. If the initial specific internal energy of the system is 450 kJ/kg, what is the final specific internal energy, in kJ/kg? Neglect ch...
1 answer

What are the domain and range of the function h(x) = -1/2(x – 4)^2 + 3?

What are the domain and range of the function h(x) = -1/2(x – 4)^2 + 3?...
2 answers

Use the following figure to answer the question. if 1 and 2 are equal then lines l and m are parrallel true or false

use the following figure to answer the question. if 1 and 2 are equal then lines l and m are parrallel true or false...
2 answers

What is the watercycle​

what is the watercycle​...
2 answers

Why did early civilizations begin in river valleys?

Why did early civilizations begin in river valleys?...
1 answer

The main differences between laptops and desktop computers other than size and portability.

The main differences between laptops and desktop computers other than size and portability....
1 answer

Which of the following terms refers to the amount of thermal energy need to change 1 kg of a substance from a liquid to a gas at its boiling point

which of the following terms refers to the amount of thermal energy need to change 1 kg of a substance from a liquid to a gas at its boiling point...
1 answer

During the year, Hamlet Inc. paid $28,000 to have bond certificates printed and engraved, paid $100,000 in legal fees, paid $11,000 to a CPA for registration information, and paid $260,000 to an underwriter as a commission. What is the amount of bond issue costs

During the year, Hamlet Inc. paid $28,000 to have bond certificates printed and engraved, paid $100,000 in legal fees, paid $11,000 to a CPA for registration information, and paid $260,000 to an underwriter as a commission. What is the amount of bond issue costs...
2 answers

Which of these factors helped Germany annex Austria? A. People in Austria wanted Germany to protect them from a French invasion. B. Germany promised to grant political rights to Austrian ethnic minorities. C. Austrian citizens felt an increasing sense of German nationalism before World War II. D. Great Britain agreed that Germany should control all German-speaking states.

Which of these factors helped Germany annex Austria? A. People in Austria wanted Germany to protect them from a French invasion. B. Germany promised to grant political rights to Austrian ethnic minorities. C. Austrian citizens felt an increasing sense of German nationalism before World War II. D...
1 answer

Raina has 3 buckets. She pours a total of 30 liters of water into these buckets. If every bucket gets the same amount, what is the volume of water in each bucket?

Raina has 3 buckets. She pours a total of 30 liters of water into these buckets. If every bucket gets the same amount, what is the volume of water in each bucket?...
1 answer

The author concludes that cabeza de vaca and the others "had been so utterly transformed" by their experience. what examples and evidence supports this conclusion?

the author concludes that cabeza de vaca and the others "had been so utterly transformed" by their experience. what examples and evidence supports this conclusion?...
1 answer

Help ASAP PLZZZZ!!!

Help ASAP PLZZZZ!!!...
1 answer

Someone please help thank u! Is the RNA an exact copy of DNA? Does it correspond to the DNA? Explain.

Someone please help thank u! Is the RNA an exact copy of DNA? Does it correspond to the DNA? Explain....
2 answers

Which of the following is the least reactive nonmetal,?

which of the following is the least reactive nonmetal,?...
2 answers

What are the two main functions of a colony?

What are the two main functions of a colony?...
2 answers

Who killed president Lincoln?

Who killed president Lincoln?...
2 answers

Who wants to play rocket league?

who wants to play rocket league?...
1 answer

How do solute concentrations affect the rate of osmosis within the cell?

How do solute concentrations affect the rate of osmosis within the cell?...
1 answer

In The Diary of Anne Frank, Act II, why does Anne leave her diary behind when the Nazis come to take the families and Mr. Dussel away? о A She is tired of writing in it. О B. She does not want it to get ruined. C. The Nazis said they could take only clothing o о D. She leaves it as a clue to where the Nazis take her.

In The Diary of Anne Frank, Act II, why does Anne leave her diary behind when the Nazis come to take the families and Mr. Dussel away? о A She is tired of writing in it. О B. She does not want it to get ruined. C. The Nazis said they could take only clothing o о D. She leaves it as a clue to wher...

-- 0.015836--