Differtentiat \( x^{2}-\frac{1}{x^{2}} \) \( w \cdot x \cdot t \)

Certainly! Let's differentiate each of the given functions with respect to \( x \). We'll assume that \( w \) and \( t \) are constants. --- ### 1. Differentiate \( f(x) = x^{2} - \frac{1}{x^{2}} \) **Function:** \[ f(x) = x^{2} - \frac{1}{x^{2}} \] **Differentiation:** \[ \frac{d}{dx} \left( x^{2} \right) = 2x \] \[ \frac{d}{dx} \left( -\frac{1}{x^{2}} \right) = -\left( -2x^{-3} \right) = \frac{2}{x^{3}} \] **Result:** \[ f'(x) = 2x + \frac{2}{x^{3}} \] --- ### 2. Differentiate \( g(x) = w \cdot x \cdot t \) **Function:** \[ g(x) = w \cdot x \cdot t \] Since \( w \) and \( t \) are constants, \( w \cdot t \) can be treated as a single constant coefficient. **Differentiation:** \[ \frac{d}{dx} \left( w \cdot x \cdot t \right) = w \cdot t \cdot \frac{d}{dx} \left( x \right) = w \cdot t \cdot 1 = w t \] **Result:** \[ g'(x) = w t \] --- **Summary of Derivatives:** 1. \(\displaystyle \frac{d}{dx} \left( x^{2} - \frac{1}{x^{2}} \right) = 2x + \frac{2}{x^{3}} \) 2. \(\displaystyle \frac{d}{dx} \left( w \cdot x \cdot t \right) = w t \) If you have any further questions or need additional clarification, feel free to ask!