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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

\int \frac{x + 4}{x ^{2} - 2 x + 1} d x

\frac{d}{d x} (arctan (\frac{x ^{2}}{y}))

11 x^{\frac{1}{2}} + x^{\frac{3}{2}}

\int_{1}^{e} ln (5 x) d x

x + 1

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