A curve has equation (x+y)^2=x*y^2, find the gradient of the curve at a point where x=1

  1. Differentiating left hand side: 2(x+y)(1+dy/dx) from the chain rule 2. Differentiating right hand side: y2+2xy(dy/dx) from the product rule 3. Equating sides and taking out factors of dy/dx to rearrange for dy/dx: dy/dx=[y2-2(x+y)]/[2(x+y)-2xy] 4. Substitute x=1 into original expression and solving for y (i.e. solving (1+y)2=y2) gives y=-1/2 5. Substituting x=1 and y=-1/2 into the expression for dy/dx gives dy/dx=-3/8
Answered by Peter K. Maths tutor

3739 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate x/(x^2+2)


integrate( x^3+4x^2+3)dx


Suppose a population of size x experiences growth at a rate of dx/dt = kx where t is time measured in minutes and k is a constant. At t=0, x=xo. If the population doubles in 5 minutes, how much longer does it take for the population to reach triple of Xo.


Given that y= 5x^2 + 2x , find dy/dx


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences