What is the derivative of x/(1+sin(x)) ?

The derivative of x/(1+sin(x)) is (1+sin(x)-xcos(x))/((1+sin(x))^2)

What is the first derivative of x/(1+sin(x)) ?

The first derivative of x/(1+sin(x)) is (1+sin(x)-xcos(x))/((1+sin(x))^2)

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\frac{d}{d x} (\frac{x}{1 + sin ( x )})

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

Solution steps

\frac{d}{d x} (\frac{x}{1 + sin ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 1 + sin ( x ) ) - \frac{d}{d x} ( 1 + sin ( x ) ) x}{( 1 + sin ( x ) ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (1 + sin (x)) = cos (x)

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

Simplify

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

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