English
Hindi

Question

Download Solution PDF

If f(x) = , then what is the derivative of f(x) ?

  3. 4x3
  4. None of these

Answer (Detailed Solution Below)

Option 3 : 4x3
Free Tests
View all Free tests >
Free
Army Havildar SAC - Quick Quiz
5 Qs. 10 Marks 6 Mins
Start Now

Detailed Solution

Download Solution PDF

Calculations:

Given, f(x) = 

f(x) = 

f(x) = x4               (∵ eloge x = x)

Taking derivative w. r. to x on both side, we get 

f'(x) = 4x3

Download Solution PDF
Latest Army Havildar SAC Updates

Last updated on Jul 1, 2025

-> The Indian Army has released the Exam Date for Indian Army Havildar SAC (Surveyor Automated Cartographer).

->The Exam will be held on 9th July 2025.

-> Interested candidates had applied online from 13th March to 25th April 2025.

-> Candidates within the age of 25 years having specific education qualifications are eligible to apply for the exam.

-> The candidates must go through the Indian Army Havildar SAC Eligibility Criteria to know about the required qualification in detail. 

Exams Tests Super Practice

More Evaluation of derivatives Questions

Q1.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q2.If \(y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^2 \alpha}\right)+\frac{1}{\sin ^2 \alpha}}\) where \(\alpha \in\left(\frac{3 \pi}{4}, \pi\right)\), then \(\frac{d y}{d \alpha}\ \rm at\ \alpha=\frac{5 \pi}{6}\) is
Q3.If f(a + b + 1 – x) = f(x) ∀x, where a and b are fixed positive real numbers, then \(\rm \frac{1}{(a+b)} \int_a^b x(f(x)+f(x+1)) d x\) is equal to
Q4.If \(\rm y=x^{\sec^2x}\times\frac{1}{x^{\tan^2x}}\), then \(\rm \frac{dy}{dx}=?\)
Q5.If y = u2 + log u and u = ex, then find \(\rm \frac{dy}{dx}:\)
Q6.If \(x=a\left(t+\frac{1}{t}\right)\) and \(y=a\left(t-\frac{1}{t}\right)\), then \(\frac{d x}{d y}\) is:
Q7.The derivative of \(\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)\) with respect to tan-1x is:
Q8.If \(y=x+\frac{x^{3}}{3}+\frac{x^{5}}{5}+\cdots\), then \(\frac{d y}{d x}\) is equal to
Q9.Find the derivative of sin−1x with respect to x assuming it to exist.
Q10.If \(\rm\frac{e^x}{1−x}\) = B0 + B1x + B2x2 + ……. + Bnxn + ……, then the value of (Bn − Bn−1) is

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:
Suggested Test Series
View All >
Army Havildar SAC Mock Test Series 2025
121 Total Tests with 3 Free Tests
Start Free Test
NCERT XI-XII Math Foundation Pack Mock Test
117 Total Tests with   4 Free Tests
Start Free Test

Army Havildar SAC Important Links

Eligibility CriteriaSalary and Job ProfileAdmit CardSyllabus and Exam PatternAnswer KeyCut Off

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 list happy teen patti teen patti gold apk download teen patti bindaas