What is the d/(dy)((1+sin(y))/(1-sin(y))) ?

The d/(dy)((1+sin(y))/(1-sin(y))) is (2cos(y))/((1-sin(y))^2)

What is the first d/(dy)((1+sin(y))/(1-sin(y))) ?

The first d/(dy)((1+sin(y))/(1-sin(y))) is (2cos(y))/((1-sin(y))^2)

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\frac{d}{d y} (\frac{1 + sin ( y )}{1 - sin ( y )})

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

Solution steps

\frac{d}{d y} (\frac{1 + sin ( y )}{1 - sin ( y )})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int 20 e^{- 0.6 t} d t

\int_{0}^{4} (2 x + 3) d x

\frac{d}{d x} (ln (\frac{x ^{2} + 1}{x + 1}))

f (x) = (x^{3} - 9 x)^{12}, at x = 3

\frac{9}{t ^{4}}

What is the d/(dy)((1+sin(y))/(1-sin(y))) ?
The d/(dy)((1+sin(y))/(1-sin(y))) is (2cos(y))/((1-sin(y))^2)
What is the first d/(dy)((1+sin(y))/(1-sin(y))) ?
The first d/(dy)((1+sin(y))/(1-sin(y))) is (2cos(y))/((1-sin(y))^2)