What is the derivative of (4sin(x)/(3+cos(x))) ?

The derivative of (4sin(x)/(3+cos(x))) is (4(1+3cos(x)))/((3+cos(x))^2)

What is the first derivative of (4sin(x)/(3+cos(x))) ?

The first derivative of (4sin(x)/(3+cos(x))) is (4(1+3cos(x)))/((3+cos(x))^2)

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\frac{d}{d x} (\frac{4 sin ( x )}{3 + cos ( x )})

\frac{4 ( 1 + 3 cos ( x ) )}{( 3 + cos ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 sin ( x )}{3 + cos ( x )})

Take the constant out:

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

= 4 \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}}

= 4 \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)

= 4 \cdot \frac{cos ( x ) ( 3 + cos ( x ) ) - ( - sin ( x ) ) sin ( x )}{( 3 + cos ( x ) ) ^{2}}

Simplify

4 \cdot \frac{cos ( x ) ( 3 + cos ( x ) ) - ( - sin ( x ) ) sin ( x )}{( 3 + cos ( x ) ) ^{2}} : \frac{4 ( 1 + 3 cos ( x ) )}{( 3 + cos ( x ) ) ^{2}}

= \frac{4 ( 1 + 3 cos ( x ) )}{( 3 + cos ( x ) ) ^{2}}

\frac{\partial}{\partial x} (x e^{- z})

\frac{\partial}{\partial x} (x^{2} ln (y))

\frac{( 3 s + 3 )}{( s ^{2} ( s + 2 ) ^{3} )}

\frac{d P}{d t} + P = 10

f (x) = 8 - x^{3}

What is the derivative of (4sin(x)/(3+cos(x))) ?
The derivative of (4sin(x)/(3+cos(x))) is (4(1+3cos(x)))/((3+cos(x))^2)
What is the first derivative of (4sin(x)/(3+cos(x))) ?
The first derivative of (4sin(x)/(3+cos(x))) is (4(1+3cos(x)))/((3+cos(x))^2)