Answers>Maths>IB>Article

Given that w=x * e^-w use implicit differentiation to show that dw/dx=1/(e^w + x)

Given that w=xe-w use implicit differentiation to show that dw/dx = 1/(ew+x)Answer:Use product rule to simplify:dw/dx = x(de-w/dx) + e-w(dx/dx)Use chain rule to simplify even further:dw/dx = -xe-w(dw/dx) + e-wWe know from the original formula that w = xe-w. Therefore, replace:dw/dx = -w*(dw/dx) + e-wRe-arrange to isolate the derivative:(dw/dx)(1+w) = e-wdw/dx = (e-w)/(1+w)Re-arrange to achieve form asked for, knowing that x = wew from original formula given:dw/dx = 1/(ew+ wew)dw/dx = 1/(ew+x)q.e.d.

Answered by Panagiota G. Maths tutor

1344 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

The velocity of a particle is given by the equation v= 4t+cos4t where t is the time in seconds and v is the velocity in m s ^-1. Find the time t when the particle is no longer accelerating for the interval 0≤t≤2.


How does the right angle triangle definition of sine, cosine and tangent relate to their graphs as a function of angle and to Euler's formula?


If the fourth term in an arithmetic sequence is, u4 = 12.5, the tenth is u10 = 27.5. Find the common difference and the 20th term.


Two functions, y1 & y2, are given by y1=x^2+16x+4; y2=2(3x+2). Find analytically the volume of the solid created by revolving the area between the two curves by 2pi radians around the x-axis. N.B. y2>y1 on the interval between the points of intersection.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences