derivative of (5sin(x)/(3+cos(x)))

解答

\frac{d}{d x} (\frac{5 sin ( x )}{3 + cos ( x )})

\frac{5 ( 1 + 3 cos ( x ) )}{( 3 + cos ( x ) ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{5 sin ( x )}{3 + cos ( x )})

将常数提出:

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

= 5 \frac{d}{d x} (\frac{sin ( x )}{3 + cos ( x )})

使用微分除法定则:

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

= 5 \cdot \frac{\frac{d}{d x} ( sin ( x ) ) ( 3 + cos ( x ) ) - \frac{d}{d x} ( 3 + cos ( x ) ) sin ( x )}{( 3 + cos ( x ) ) ^{2}}

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (3 + cos (x)) = - sin (x)

= 5 \cdot \frac{cos ( x ) ( 3 + cos ( x ) ) - ( - sin ( x ) ) sin ( x )}{( 3 + cos ( x ) ) ^{2}}

化简

5 \cdot \frac{cos ( x ) ( 3 + cos ( x ) ) - ( - sin ( x ) ) sin ( x )}{( 3 + cos ( x ) ) ^{2}} : \frac{5 ( 1 + 3 cos ( x ) )}{( 3 + cos ( x ) ) ^{2}}

= \frac{5 ( 1 + 3 cos ( x ) )}{( 3 + cos ( x ) ) ^{2}}

\int_{1}^{4} (2 x + x) d x

\int \frac{2 e ^{3 t}}{1 + e ^{6 t}} d t

x \to 2 + lim (\frac{∣ x ∣ + 2}{x - 2})

x \frac{d y}{d x} = y - x

x \to 0 lim (\frac{( cos ( 2 x ) - cos ( 3 x ) )}{x ^{2}})