The curve C has equation 4x^2 – y^3 – 4xy + 2^y = 0 The point P with coordinates (–2, 4) lies on C . Find the exact value of dy/dx at the point P .

Since we need to find dy/dx, we must first differentiate the equation implicitly which gives us: 8x - 3y2dy/dx - 4y - 4xdy/dx + 2yln(2)dy/dx = 0. Because we are given a point, we can substitute in the x and y values of that point which results in: -16 - 48dy/dx - 16 + 8dy/dx + 16ln(2)dy/dx = 0.We now have an equation which is easily solved by rearrangement. First we bring all dy/dx's to one side: 16ln(2)dy/dx - 40dy/dx = 32. And then we isolate dy/dx: dy/dx(16ln(2) - 40) = 32 => dy/dx = 32/(16ln(2) - 40).

SN
Answered by Samuel N. Maths tutor

7968 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?


x is an angle, if 180 > x > 90 and sinx = √2 / 4 what is the value of angle x


What are logarithms?


Find the exact solution of the following equation: e^(4x-3) = 11


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