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.
If the side of a square can be expressed as a2b 3 , what is the area of the square in simplified form? Since the formula for the area of a square is A = s 2 , then by substitut
A bucket of height 8 cm and made up of copper sheet is in the form of frustum of right circular cone with radii of its lower and upper ends as 3 cm and 9 cm respectively. Calculate
how do you subtract 2 1\8 from 5\16
I need help with my calculus
How do you multiply frations?
Given that 2t 2 y′′ + ty′ - 3 y = 0 Show that this given solution are form a fundamental set of solutions for the differential equation? Solution The two solutions f
There's a nice way to show why the expresion for the area of a circle of radius R is: Pi * R 2 . It has an comman relationship with the experation for the circumference of a
A reliability system consists of 15 independent components. The probability that a component works is 0.9 for each. The system works if at least 11 of the components work. Fi
Linear Equations We'll begin the solving portion of this chapter by solving linear equations. Standard form of a linear equation: A linear equation is any equation whi
Series - The Basics That topic is infinite series. So just define what is an infinite series? Well, let's start with a sequence {a n } ∞ n=1 (note the n=1 is for convenie
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