Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
Differentiate y = x x
Solution : We've illustrated two functions similar to this at this point.
d ( xn ) /dx = nxn -1 d (a x ) /dx= a x ln a
Neither of these two can imply here since both need either the base or the exponent to be a constant. In this case the base and the exponent both are variables and thus we have no way to differentiate this function by using only known rules from earlier sections.
However, with logarithmic differentiation we can do this. First take logarithm of both sides and utilize the logarithm properties to simplify things a little.
ln y = ln x x
ln y = x ln x
Differentiate both sides by using implicit differentiation.
y′ / y = ln x + x ( 1 /x)= ln x + 1
As along the first example multiply through y & substitute back in for y.
y′ = y (1 + ln x )
= x x (1 + ln x )
We'll close this section out with a quick recap of all the various ways we've seen of differentiating functions along with exponents. It is significant to not get all of these confused.
Two boys A and B are at two diametrically opposite points on a circle. At one instant the two start running on the circle; A anticlockwise with constant speed v and B clockwise wit
The given figure consists of four small semicircles and two big semicircles. If the smaller semicircles are equal in radii and the bigger semicircles are also equal in radii, find
Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 35°N and New Orleans has latitude 30°N. Find the distance between these
Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot. If α , β be the elevations of the top of the tower from these
Suppose that at some future time every telephone in the world is assigned a number that contains a country code, 1 to 3 digits long, that is, of the form X, XX , XXX or followed
Consider the wave equation u_tt - u_xx = 0 with u(x, 0) = f(x) = 1 if -1 Please provide me a detailed answer. I had worked the most part of this question and the only I would like
Hi may i know how to substract the (ID)colum matrix from (K)square matrix as per equation below. E = (K - ID)^-1 S K is m*m matrix I is idntity matrix d is column vector s is col
The height of a rectangle is 20 cm. The diagonal is 8 cm more than the length. Determine the length of the rectangle. a. 20 b. 23 c. 22 d. 21 d. To determine the len
Everything stored on a computer can be represented as a string of bits. However, different types of data (for example, characters and numbers) may be represented by the same strin
All about fractions
Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!
whatsapp: +91-977-207-8620
Phone: +91-977-207-8620
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd