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.
Graphical Understanding of Derivatives: A ladder 26 feet long is leaning against a wall. The ladder begins to move such that the bottom end moves away from the wall at a const
Example of Integration by Parts - Integration techniques Some problems could need us to do integration by parts many times and there is a short hand technique that will permit
i needed help with algebra
suresh invested rs.1080 in shares of face value rs.50 at rs.54.After receiving dividend on them at 8% he sold them at 52.In each of the transaction he paid 2 % brokerage.Hpw much d
Question: Classify the following differential equations as linear/nonlinear. Also, what is the order of the following differential equations? Xy'-2y =x Xy'' -2y' =xsin(y)
Determine if the following sequences converge or diverge. If the sequence converges find out its limit. a. {3n 2 - 1 / 10n + 5n 2 } ∞ n =2 b. {e 2n / n} ∞ n =1 c
Velocity : Recall that it can be thought of as special case of the rate of change interpretation. If the situation of an object is specified by f(t ) after t units of time the vel
"Standard" trig equation: Now we need to move into a distinct type of trig equation. All of the trig equations solved to this point were, in some way, more or less the "standard"
how does it work?
carlie is now fivetimes as old as henry. in nine years her age will be twice henry''s age then. how old is carly now
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