Find dy/dx from the equation 2xy + 3x^2 = 4y
Firstly we must notice that we can differentiate each term separately.
Starting with the 2xy term, we must use the product rule as x and y are two variable that will differentiate. Setting u=2x and v=y and using (uv)'= uv' + vu' we get the term 2y+2xy'.
For the 3x^2 term, we can differentiate as usual to get 6x.
For the 4y term, we can simply differentiate to get 4y'.
Putting this all together we get: 2y+2xy'+6x=4y'.
Finally, rearranging gives dy/dx=(3x+y)/(2-x)
MM
Related Maths A Level answers
All answers ▸A curve has parametric equations: x = 3t +8, y = t^3 - 5t^2 + 7t. Find the co-ordinates of the stationary points.
Using the identity cos(A+B)= cosAcosB-sinAsinB, prove that cos2A=1-2sin^2A.
The straight line L1 passes through the points (–1, 3) and (11, 12). Find an equation for L1 in the form ax + by + c = 0, where a, b and c are integers
Integrate the function 1/sqrt(9-x^2) with respect to x