(\partial)/(\partial x)((F(c,x,b)cos(c))/(xb))

解

\frac{\partial}{\partial x} (\frac{F ( c , x , b ) \cdot cos ( c )}{x \cdot b})

\frac{cos ( c )}{b} \cdot \frac{\frac{\partial}{\partial x} ( F ( c , x , b ) ) x - 1 \cdot F ( c , x , b )}{x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (\frac{F ( c , x , b ) cos ( c )}{x b})

c, b

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{cos ( c )}{b} \frac{\partial}{\partial x} (\frac{F ( c , x , b )}{x})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{cos ( c )}{b} \cdot \frac{\frac{\partial}{\partial x} ( F ( c , x , b ) ) x - \frac{\partial}{\partial x} ( x ) F ( c , x , b )}{x ^{2}}

\frac{\partial}{\partial x} (x) = 1

= \frac{cos ( c )}{b} \cdot \frac{\frac{\partial}{\partial x} ( F ( c , x , b ) ) x - 1 \cdot F ( c , x , b )}{x ^{2}}