First slide

Derivatives

Question

$If (x + y)^{m + n} = x^{m} y^{n} then \frac{d y}{d x} =$

Moderate

A

$\frac{x}{y}$
B

$- \frac{y}{x}$
C

$- \frac{x}{y}$
D

$\frac{y}{x}$

Solution

$\begin{array}{l} (m + n) \log (x + y) = m \log x + m \log y \\ \frac{d y}{d x} = \frac{- (\partial f / \partial x)}{(\partial f / \partial y)} = \frac{- [\frac{m + n}{x + y} - \frac{m}{x}]}{\frac{m + n}{x + y} - \frac{m}{y}} = \frac{- [n x - m y] \cdot y}{(m y - n x) x} = \frac{y}{x} \end{array}$

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