Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3 - Page 140: 24

$\dfrac{dy}{dx}$ at $x=1$ is $\boxed{96}$.

$y=x^{24}+2x^{12}+3x^8+4x^6$ Taking the derivative of the polynomial: $\dfrac{dy}{dx}=(24)x^{24-1}+2(12)x^{12-1}+3(8)x^{8-1}+4(6)x^{6-1}=24x^{23}+24x^{11}+24x^7+24x^5$ Plugging in $x=1$, $24(1)^{23}+24(1)^{11}+24(1)^7+24(1)^5=24+24+24+24=\boxed{96}$