Using implicit differentiation, write the expression "3y^2 = 4x^3 + x" in terms of "dy/dx"

To differentiate this expression with respect to "x", any terms comprising of an "x" must multiply their powers with their numerical values and subtract 1 from the power. However to differentiate a non-"x" term with respect to "x" we need to do it differently. The value of the "y" term must be multiplied by "dy/dx" before it can be differentiated as normal. The process looks like this:
3y2 -> 3y2 (dy/dx) -> 6y(dy/dx). Therefore the differential is 6y(dy/dx) = 12x2 + 1. However, the question asks for the answer in terms of "dy/dx", so we must manipulate the expression by dividing both sides by "6y". Then we get the final answer of:dy/dx = (12x2 + 1)/6y.

BW
Answered by Brendan W. Maths tutor

3516 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Given that x = cot y, show that dy/dx = -1/(1+x^2)


If a 5 metre ladder is resting against a wall and the bottom of the ladder is 3 metres away from the wall, and someone pulls the bottom of the ladder away at a speed of 1 metre per second, calculate the speed of the top of the ladder after t seconds


How can we simplify sqrt(48) - 6/sqrt(3) ?


Find the equation of the line perpendicular to the line y= 3x + 5 that passes through the point (-1,4)


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