The curve C has equation 2yx^2 + 2x + 4y - cos(πy) = 45. Using implicit differentiation, find dy/dx in terms of x and y

2x2y + 2x + 4y - cos(πy) = 45Applying implicit differentiation:4xy + 2x2(dy/dx) + 2 + 4(dy/dx) + πsin(πy)(dy/dx) = 0Moving all (dy/dx) terms to one side:2x2 (dy/dx) + 4(dy/dx) + πsin(πy)(dy/dx) = -4xy - 2Factorising:dy/dx [ 2x2 + 4 +πsin(πy) ] = -(4xy + 2)Making (dy/dx) the subject of the equation:dy/dx = -(4xy + 2) / 2x2 + 4 +πsin(πy)

PM
Answered by Prahlad M. Maths tutor

5671 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate: y = 3x^2 + 4x + 1 -4x^-1


A curve has equation y = f(x) and passes through the point (4, 22). Given that f ′(x) = 3x^2 – 3x^(1/2) – 7, use integration to find f(x), giving each term in its simplest form.


Find the derivative of f(x)=exp((tanx)^(1/2))


Solve Inx + In3 = In6


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning