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 tanA+sinA=m and tanA-sinA=n, show that m 2 -n 2 = 4√mn Ans: TanA + SinA = m TanA - SinA = n. m 2 -n 2 =4√mn . m 2 -n 2 = (TanA + SinA) 2 -(TanA - SinA) 2
a lending library has a fixed charge for the first three days and an additional charge for each day thereafter. sam paid Rs 27 for a bookkept for 7 days while jaan paid Rs 21 for t
Euler''''s Constant (e) Approximate the number to the one hundredth, one ten-thousandths, and one one-hundred-millionth.
divid
The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to
a business is owned by three people.the first owns 1/12 of the business and the second owns 1/6 of the business. what fractional part of the business is owned by the third person
#question when equation of tangent T=0 and why
a company''s advertising expenditures average $5,000 per month. Current sales are $29,000 and the saturation sales level is estimated at $42,000. The sales-response constant is $2,
RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS, ST, AND RT
The King Company is producing two types of products: A and B. Both products are produced on the similar machining operation. The machines operate on two 8-hour shifts, 5 days per w
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