The process of evaluating the derivative is essentially determining the rate of change of a function at any specific point. This critical calculus concept is usually denoted as f'(x) or dy/dx. There are several rules used to compute derivatives, including the power rule, product rule, quotient rule, and chain rule.
| Topic | Problem | Solution |
|---|---|---|
| None | Determine the rate of change on the interval $(3,… | Determine the rate of change on the interval $(3,7)$ using the graph below: |
| None | Suppose $h(x)=2 f(2 \tan (x))+2 f(6+3 \sin (x))$.… | Suppose \(h(x)=2 f(2 \tan (x))+2 f(6+3 \sin (x))\). You are also told that \(f(0)=40\) and \(f(6)=2… |
| None | If $f^{\prime}(x)=\frac{2}{x^{2}}$ then... A. $f(… | The question is asking for the antiderivative of the function \(f^{\prime}(x)=\frac{2}{x^{2}}\). Th… |
| None | Let $y=\tan (5 x+2)$. Find the differential $d y$… | Given the function \(y = \tan(5x + 2)\), we need to find the differential \(dy\) when \(x=5\) and \… |
| None | If $f(x)=\sin ^{-1}(x)$, then what is the value o… | Given the function $f(x) = \sin^{-1}(x)$, we need to find the derivative $f'(x)$ and then evaluate … |
| None | 14 Given $f(x)=x\left(1-3 x^{2}\right), f^{\prime… | Given the function \(f(x) = x(1 - 3x^2)\), we want to find \(f^\prime(-1)\). |
| None | \( f^{\prime}(2), f^{\prime}(x) \) ج \( f(x)=\lef… | \(f'(x) = \frac{3}{2}(x^3 + 3x^2 - 3)^{\frac{1}{2}} \times (3x^2 + 6x)\) |