Differentiate the function. \[ g(x)=\frac{3}{8} x^{2}-8 x+15 \] \( g^{\prime}(x)=\square \) Read it Master it

To differentiate the function \( g(x) = \frac{3}{8} x^{2} - 8x + 15 \), we apply the power rule. The derivative of \( \frac{3}{8} x^{2} \) is \( \frac{3}{4} x \), the derivative of \( -8x \) is \( -8 \), and the derivative of the constant \( 15 \) is \( 0 \). So, putting it all together, we get: \( g^{\prime}(x) = \frac{3}{4} x - 8 \). Many students get tripped up with constants! Remember, when you're differentiating, constants drop away like autumn leaves. That’s why you don’t see a derivative for \( 15 \) in the final answer. Just think of it as nature's way of reminding you to keep things moving! Also, be careful with your signs! When differentiating linear and quadratic terms, it can get easy to forget if you're subtracting or adding coefficients, especially under exam pressure. A small sign mistake can change everything, so double-check your work—your future self will thank you!