What is the derivative of (sin(x)/(7+cos(x))) ?

The derivative of (sin(x)/(7+cos(x))) is (cos(x)(7+cos(x))+sin^2(x))/((7+cos(x))^2)

What is the first derivative of (sin(x)/(7+cos(x))) ?

The first derivative of (sin(x)/(7+cos(x))) is (cos(x)(7+cos(x))+sin^2(x))/((7+cos(x))^2)

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\frac{d}{d x} (\frac{sin ( x )}{7 + cos ( x )})

\frac{cos ( x ) ( 7 + cos ( x ) ) + sin ^{2} ( x )}{( 7 + cos ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{sin ( x )}{7 + cos ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( sin ( x ) ) ( 7 + cos ( x ) ) - \frac{d}{d x} ( 7 + cos ( x ) ) sin ( x )}{( 7 + cos ( x ) ) ^{2}}

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

\frac{d}{d x} (7 + cos (x)) = - sin (x)

= \frac{cos ( x ) ( 7 + cos ( x ) ) - ( - sin ( x ) ) sin ( x )}{( 7 + cos ( x ) ) ^{2}}

Simplify

\frac{cos ( x ) ( 7 + cos ( x ) ) - ( - sin ( x ) ) sin ( x )}{( 7 + cos ( x ) ) ^{2}} : \frac{cos ( x ) ( 7 + cos ( x ) ) + sin ^{2} ( x )}{( 7 + cos ( x ) ) ^{2}}

= \frac{cos ( x ) ( 7 + cos ( x ) ) + sin ^{2} ( x )}{( 7 + cos ( x ) ) ^{2}}

\frac{d}{d x} (5 + 6 x^{\frac{3}{2}})

x^{^{''}} + 4 x = 3

\int \frac{7}{x ^{3} - 27} d x

x \to 4 lim (- \frac{3}{( x - 4 ) ^{2}})

\frac{\partial}{\partial x} (5)

What is the derivative of (sin(x)/(7+cos(x))) ?
The derivative of (sin(x)/(7+cos(x))) is (cos(x)(7+cos(x))+sin^2(x))/((7+cos(x))^2)
What is the first derivative of (sin(x)/(7+cos(x))) ?
The first derivative of (sin(x)/(7+cos(x))) is (cos(x)(7+cos(x))+sin^2(x))/((7+cos(x))^2)