## Calculus, 10th Edition (Anton)

$\left[ \frac{dy}{dx}\right]_{x=1} = 15$
Let $y = 1 + x + x^2 + x^3 + x^4 + x^5$. $$\frac{dy}{dx} = 0 + 1 + 2x + 3x^2 + 4x^3 + 5x^4$$ Now, let us evaluate the value of the derivative at $x = 1$: \begin{align} \frac{dy}{dx}|_{x=1} &= 0 + 1 + 2\cdot 1 + 3 \cdot 1^2 + 4\cdot1^3 + 5\cdot1^4 \\ &= 1 + 2 + 3 + 4 + 5 \\ &= 15 \end{align}