Differentiate the function \( G(x)=2 x^{-4}+3 x^{-5} \)

To find the derivative of the function \( G(x) = 2x^{-4} + 3x^{-5} \), we can use the power rule. The derivative of \( x^n \) is \( nx^{n-1} \). Applying this rule, we get: \[ G'(x) = 2 \cdot (-4)x^{-5} + 3 \cdot (-5)x^{-6} = -8x^{-5} - 15x^{-6} \] So, the final answer is \( G'(x) = -8x^{-5} - 15x^{-6} \). Now that we've differentiated, let's explore! Understanding how derivatives work can be a game-changer in fields like physics, where they help describe motion and change. For instance, when analyzing how fast an object is moving or what its acceleration is, derivatives provide essential insights! If you're diving deeper into calculus, "Calculus Made Easy" by Silvanus P. Thompson is a fantastic, user-friendly guide. It breaks down complex concepts into approachable chunks and is perfect for beginners eager to master calculus in a fun way. Happy reading!