Find dy/dx when x+2y+3y^2= 2x^2+1

To solve this question we can use implicit differentiation. We can write:d/dx(x+2y+3y^2)=d/dx(2x^2+1).When differentiating something in terms of y with respect to x we can use the chain rule, this allows us to differentiate with respect to y and multiply by dy/dx. 1+(d(2y)/dy)*dy/dx+(d(3y^2)/dy)*dy/dx=4x, then we differentiate our y values with respect to y: 1+2dy/dx+(6y)dy/dx=4x. Then we need to set dy/dx as the subject of the equation:dy/dx(2+6y)=4x-1, then by dividing each side by (2+6y) we get dy/dx=(4x-1)/(2+6y).

AG
Answered by Adam G. Maths tutor

3205 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The probability distribution of the random variable X is given by the formula P(X = x) = 0.09+0.01x^2 for x= 1,2,3,4,5 ). Find E(X).


Prove, using the product rule that, the derivative of x^{n} is nx^{n-1} where n is a natural number. What if n is an integer or n is rational?


The volume, V, of water in a tank at time t seconds is given by V = 1/3*t^6 - 2*t^4 + 3*t^2, for t=>0. (i) Find dV/dt


The point P (4, –1) lies on the curve C with equation y = f( x ), x > 0, and f '(x) =x/2 - 6/√x + 3. Find the equation of the tangent to C at the point P , giving your answer in the form y = mx + c. Find f(x)


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