Implicit Differentiation

Question

If x² + y² = 25, then dy/dx equals

RankGuru · Accepted Answer

1. **Method**: Differentiate both sides of the equation with respect to $x$.
2. **Perform Differentiation**:
   - $\frac{d}{dx}(x^2) + \frac{d}{dx}(y^2) = \frac{d}{dx}(25)$
   - $2x + 2y \frac{dy}{dx} = 0$
3. **Isolate $dy/dx$**:
   - $2y \frac{dy}{dx} = -2x$
   - $\frac{dy}{dx} = -\frac{2x}{2y} = -\frac{x}{y}$.
- This derivative gives the slope of the tangent to a circle of radius 5 at any point $(x, y)$.

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Implicit Differentiation

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