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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int_{0}^{2} 4 t d t

f (x) = \frac{4 x - 3}{5 x ^{2} + 3 x}

\int x sin^{3} (x) d x

\int x^{2} arctan (x) d x

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