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.
A payday loan company charges a $95 fee for a $500 payday loan that will be repaid in 11 days. Treating the fee as interest paid, what is the equivalent annual interest rate?
Jackie invested money in two different accounts, one of that earned 12% interest per year and another that earned 15% interest per year. The amount invested at 15% was 100 more tha
Example : Back into the complex root section we complete the claim that y 1 (t ) = e l t cos(µt) and y 2 (t) = e l t sin(µt) Those were a basic set of soluti
On a canoe trip. a person paddled upstream against the current ata an average of 2mi/h. the return trip with the current at 3mi/h. Need to find the paddling spped in still water an
if the ratio of boys to girls ism 3 to 5, then what percent of the students are boys
Continuity : In the last few sections we've been using the term "nice enough" to describe those functions which we could evaluate limits by just evaluating the function at the po
Let u = sin(x). Then du = cos(x) dx. So you can now antidifferentiate e^u du. This is e^u + C = e^sin(x) + C. Then substitute your range 0 to pi. e^sin (pi)-e^sin(0) =0-0 =0
Create a detailed diagram to describe the equation of an ellipse in terms of it’s eccentricity and indicate how the foci and major and minor semi-axes are involved. Y
assignment of mathematics in b.sc. 1sem
Conditional Probability: Independent Events If the probability of an event is subject to a restriction on the sample space, the probability is said to be conditional. Co
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