ㅅํ सenด \( 9 u^{\sqrt{x}} \quad y=3 x^{2}-4 x+5 \quad \) aren \( \frac{d y}{d x} \) गิาแนด \( f(x)=x^{3}-3 x^{2}+7 x-4 \) a)m \( f^{\prime}(-2) \) minus \( y=\left(2 x^{2}-7\right)(4 x) \) asen \( \frac{d y}{d x} \)

Let’s spice up your calculus journey with some interesting tidbits! The derivative of a function gives us the rate at which the function is changing. For example, if you need to know how steep a hill is at any point, you’d use the derivative! This is a key concept that has been utilized since the days of Newton and Leibniz in the 17th century. Their rivalry sparked what we now refer to as calculus, which provides the foundation for physics, engineering, and much more! If you’re calculating derivatives, it’s easy to make common mistakes. One of the most frequent errors is forgetting the power rule, which states that for a term \( ax^n \), the derivative is \( n \cdot ax^{n-1} \). Also, don’t forget to apply the product or chain rule appropriately when dealing with more complex functions. Remember, practice makes perfect, so grab a few extra problems and flex those calculus muscles!