The Quotient Rule represents a technique in calculus, used to identify the derivative of a fraction. If you are dealing with a function that is the quotient of two distinct functions, expressed as f(x) = g(x) / h(x), the derivative can be determined by employing the quotient rule: [h(x) * g'(x) - g(x) * h'(x)] / [h(x)]^2.
| Topic | Problem | Solution |
|---|---|---|
| None | Let $p$ and $q$ be piecewise linear functions giv… | Given that \(r(x)=\frac{q(x)}{p(x)}\), we can use the quotient rule to find the derivative. The quo… |
| None | Find the slope of the secant line between the val… | Given the function \(f(x)=\frac{4 x+3}{5 x+5}\) and the points \(x_{1}=6\) and \(x_{2}=-10\) |
| None | Calculate $\frac{d y}{d x}$. You need not expand … | Given the function \(y=\frac{7 x^{2}-9 x+13}{2 x+4}\), we are asked to find the derivative of this … |
| None | Find $f_{x}$ and $f_{y}$ for $f(x, y)=\frac{4 x}{… | Given the function \(f(x, y)=\frac{4 x}{9 y}-\frac{2 y}{5 x}\), we need to find the partial derivat… |
| None | Differentiate the function. \[ y=\frac{3 x^{2}-5}… | We are given the function \(y=\frac{3 x^{2}-5}{2 x^{3}+3}\) and we are asked to find its derivative. |
| None | Differentiate and simplify: $f(x)=\frac{\ln e^{x}… | Given the function \(f(x)=\frac{\ln e^{x}}{e^{x}}\) |
| None | Find the first and second derivatives. \[ y=\frac… | We are given the function \(y = \frac{2x^5 + 6}{x^3}\). |
| None | $\left(\frac{x+3}{(x+1)}\right)^{\prime}$ | Given function: \(\frac{x+3}{x+1}\) |