Question

Download Solution PDF

If xy = ex - y , then find the value of  

Answer (Detailed Solution Below)

Option 3 :

Detailed Solution

Download Solution PDF

Calculation:

xy = ex - y 

Taking log on both sides, we get 

⇒ xy = log ex - y 

⇒ y log x = (x - y) loge e 

⇒ y log x = x - y             [∵ loge e = 1]

⇒ ( 1 + log x)y = x  

⇒ y = 

Differentiating both sides , we get

 =    

=  

= 

Download Solution PDF
Exams Tests Super Practice

More Differentiation by taking log Questions

Q1.If \(\frac{dy}{dx} = (\ln 5)y \)  with y(0) = ln 5, then what is y(1) equal to?
Q2.If y = (xx)x, then what is the value of \(\frac{dy}{dx}\) at x = 1?
Q3.If xyyx = 1, then what is \(\frac{dy}{dx}\) at (1, 1) equal to?
Q4.If f(x) = \(\rm (\log x)^{\sin x}\), find the value of f'(x).
Q5.\(\rm \frac{d}{dx}x^{2x}\) = 
Q6.If xy = ex - y , then find the value of \(\frac{\mathrm{d} \rm y}{\mathrm{d} x}\) 
Q7. If xm yn = 2(x + y)m + n , find the value of \(\frac{\mathrm{d} y}{\mathrm{d} x} \)
Q8.What is the value of f''(x) for f(x) = xx
Q9.What will be the value of y'(x) given that y = xln x?

More Differential Calculus Questions

Q1.What is g’(0) equal to? 
Q2.What is h’(0) equal to? 
Q3.What is the least value of f(x)? 
Q4.What is the greatest value of f(x)? 
Q5.What is the maximum value of a cos x + b sin x + c? 
Q6.What is the minimum value of the function f(x) = log10(x2 + 2x + 11)? 
Q7.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q8.The growth model for a population is Nt = N0ert where Nt is the population at time t, N0 is the initial population and r is the per capita growth rate. How long does it take for the population numbers to double?
Q9.Suppose that the growth rate of the number of individuals (N) in a population in an environment with a carrying capacity K is modelled as \(\frac{d N}{d t}=r N \frac{K-N}{K}\) where r is the per capita growth rate and t is time; r and K are positive constants. At which of the following values of N will the population growth rate be the maximum?
Q10.The population P = P(t) at time ‘t’ of a certain species follows the differential equation dP/dt = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is:

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti baaz teen patti master new version teen patti joy 51 bonus teen patti list teen patti flush