Differticate \( \operatorname{ten}^{-1} x \) wird \( \operatorname{cof}^{-1} x \)

To differentiate \( \operatorname{ten}^{-1} x \) and obtain \( \operatorname{cof}^{-1} x \), follow these steps: 1. **Identify the Operators**: Ensure \( \operatorname{ten} \) is differentiable and invertible. 2. **Apply the Inversion Rule**: \[ \frac{d}{dx} \operatorname{ten}^{-1}(x) = -\operatorname{ten}^{-1}(x) \cdot \frac{d}{dx} \operatorname{ten}(x) \cdot \operatorname{ten}^{-1}(x) \] 3. **Relate to Cofactor**: If \( \operatorname{cof} \) is related to the adjugate or cofactor matrix, express the derivative in terms of cofactors by differentiating the adjugate and determinant. For a matrix example: \[ \frac{d}{dx} A^{-1} = -A^{-1} \cdot \frac{dA}{dx} \cdot A^{-1} \] where \( A \) is a differentiable invertible matrix. If more context is provided about \( \operatorname{ten} \) and \( \operatorname{cof} \), a more specific solution can be given.