Calculus I, Fall 2014 (http://www.math.nthu.edu.tw/~wangwc/)

Brief answer to selected problems in HW04

1. Hw04: Problem 2

\frac{d}{dx}f(g(2)) = f′(g(2))g′(2) = 4 × 0.1 = 0.4

2. Section 3.7: Problem 42. Using implicit differentiation to get

\frac{dy}{dx} = \frac{y + 2}{1 − x}

And normal parallel to the line 2x + y = 0 lead us to solve the equations

\{ \begin{matrix}\frac{y+2}{1−x} = \frac{1}{2} \\ xy + 2x − y = 0 \end{matrix}

3. Section 3.7: Problem 48. Implicit differentiation gives us

qy^{q−1} \frac{dy}{dx} = px^{p−1}

By using y = x^{\frac{p}{q}} to express \frac{dy}{dx} leads to the result.