If x^2 + 4x + 3xy + y^3 = 6, find the first derivative.
This is an example of implicit differentiation. We differentiate with respect to x, remembering that y is a function of x. The terms without a 'y' differentiate as normal by the power rule nxn-1. This is the terms x2, 4x and the 6 on the other side of the = sign which goes to zero as it is a constant. y differentiates to dy/dx so the product rule is used on the term 3xy and the chain rule is used on the term y3. 2x + 4 + 3x*dy/dx + 3y + 3y2dy/dx = 0 As dy/dx is a product in two of the terms, we can factorise this out. dy/dx(3x + 3y2) = -(2x +3y + 4)dy/dx = -(2x + 3y + 4)/(3x + 3y2)
TD
Related Maths A Level answers
All answers ▸Water is flowing into a rightcircular cone at the rate r (volume of water per unit time). The cone has radius a, altitude b and the vertex or "tip" is pointing downwards. Find the rate at which the surface is rising when the depth of the water is y.
How come x^2 = 25 has 2 solutions but x=root(25) only has one? Aren't they the same thing?
Differentiate 2e^(3x^2+6x)
Integration by parts: Integrate the expression x.ln(x) between 1 and 2.