What is the derivative of (2sin(x)/(3+cos(x))) ?

The derivative of (2sin(x)/(3+cos(x))) is (2(1+3cos(x)))/((3+cos(x))^2)

What is the first derivative of (2sin(x)/(3+cos(x))) ?

The first derivative of (2sin(x)/(3+cos(x))) is (2(1+3cos(x)))/((3+cos(x))^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{2 sin ( x )}{3 + cos ( x )})

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

Solution steps

\frac{d}{d x} (\frac{2 sin ( x )}{3 + cos ( x )})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{sin ( x )}{3 + cos ( x )})

Apply the Quotient Rule:

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

= 2 \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)

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

Simplify

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

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

y = 96 x^{2} + 72 x + 12

y^{^{'}} cos (x) = y sin (x) + sin (103 x)

(x + 2 x) (2 x + 1)

\frac{d y}{d x}, 1 + ln (9 x y) = e^{(9 x - y)}

\int \frac{31}{x ( x ^{2} + 4 ) ^{2}} d x

What is the derivative of (2sin(x)/(3+cos(x))) ?
The derivative of (2sin(x)/(3+cos(x))) is (2(1+3cos(x)))/((3+cos(x))^2)
What is the first derivative of (2sin(x)/(3+cos(x))) ?
The first derivative of (2sin(x)/(3+cos(x))) is (2(1+3cos(x)))/((3+cos(x))^2)