\( h ^ { \prime } ( x ) = e ^ { x } + \frac { 1 } { x ^ { 2 } } \)

Did you know that derivatives like the one you’ve encountered have real-world applications in various fields? Take physics, for instance; they help us understand how things change over time! The derivative \( h'(x) \) indicates how the function \( h(x) \) changes with respect to \( x \). It’s like tracking the speed of a car—where the \( e^x \) part can signify continuous growth, and \( \frac{1}{x^2} \) highlights a diminishing influence as \( x \) increases! If you’re diving into derivatives and working with \( h'(x) \), be careful not to mix up exponential and polynomial rules! A common mistake is forgetting that the derivative of \( e^x \) is itself, while \( \frac{1}{x^2} \) falls under the power rule. Make sure to differentiate each term separately and check your algebra afterward—precision is your best friend in calculus!