Implicit Differentiation Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

easy
Find dydx\frac{dy}{dx} for x2+3y2=7x^2 + 3y^2 = 7.

Solution

  1. 1
    Differentiate: 2x+6ydydx=02x + 6y\frac{dy}{dx} = 0.
  2. 2
    dydx=−x3y\frac{dy}{dx} = -\frac{x}{3y}.

Answer

dydx=−x3y\frac{dy}{dx} = -\frac{x}{3y}
Differentiate term by term. The 3y23y^2 term gives 6y dydx6y\,\frac{dy}{dx} by the chain rule. Solve for dydx\frac{dy}{dx}.

About Implicit Differentiation

Finding dydx\frac{dy}{dx} when yy is defined implicitly by an equation like F(x,y)=0F(x, y) = 0, by differentiating both sides and solving for dydx\frac{dy}{dx}.

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More Implicit Differentiation Examples

Example 1 easy

Find [formula] for the circle [formula] and evaluate it at the point [formula].

Example 2 hard

Find [formula] for [formula] (folium of Descartes).

Example 3 medium

Find [formula] for the circle [formula].

Example 5 medium

Find the equation of the tangent line to [formula] at the point [formula].

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