The technique of implicit differentiation is a valuable tool in calculus that enables us to calculate derivatives for functions that are defined implicitly, rather than in an explicit manner. By applying the chain rule and regarding dependent variables as functions of independent ones, we can deal effectively with equations that are not readily expressible as functions. This method is frequently employed in the field of calculus.
| Topic | Problem | Solution |
|---|---|---|
| None | Evaluate the derivative of the following function… | We are given the function \(18x^{3}y^{2} - 6y^{3} = 1458\) and we are asked to find the derivative … |
| None | (c) Find $\frac{d y}{d x}$ where $x+y+\sqrt{x y}=… | Understand the problem: We are asked to find the derivative of y with respect to x, given the equat… |
| None | Use implicit differentiation to find $y^{\prime}$… | First, we differentiate both sides of the equation with respect to \(x\). |
| None | Differentiate implicitly to find $\frac{d^{2} y}{… | First, we need to differentiate the given equation implicitly with respect to \(x\). The given equa… |
| None | Differentiate implicitly to find $\frac{d y}{d x}… | Given the equation \(x^{2}-3 y^{2}=-4\), we can differentiate both sides with respect to \(x\). |
| None | Differentiate implicitly to find $\frac{d y}{d x}… | Differentiate both sides of the equation \(y^{2}-x^{3}=28\) with respect to x. For the left side, u… |
| None | Suppose that $x$ and $y$ are related by the given… | Given the equation \(x^{7} y+y^{7} x=9\), we need to find \(\frac{d y}{d x}\). |
| None | $\frac{d y}{d x}(2 y)$ | The question is asking for the derivative of the function \(2y\) with respect to \(x\). Since \(y\)… |