Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3 - Page 140: 21

$\frac{dy}{dx}|_{x=1} = 15$

We use the power rule as follows: $y = 1 + x + x^2 + x^3 + x^4 + x^5$ $\frac{dy}{dx} = 0 + 1 + 2x + 3x^2 + 4x^3 + 5x^4 = 1 + 2x + 3x^2 + 4x^3 + 5x^4$ We then evaluate this derivative at $x=1$: $\frac{dy}{dx}|_{x=1} = 1 + 2(1) + 3(1^2) + 4(1^3) + 5(1^4) = 1 + 2 + 3 + 4 + 5 = 15$