What is the d/(da)((cos^2(a))/(sin(a)-1)) ?

The d/(da)((cos^2(a))/(sin(a)-1)) is (-sin(2a)(sin(a)-1)-cos^3(a))/((sin(a)-1)^2)

What is the first d/(da)((cos^2(a))/(sin(a)-1)) ?

The first d/(da)((cos^2(a))/(sin(a)-1)) is (-sin(2a)(sin(a)-1)-cos^3(a))/((sin(a)-1)^2)

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

\frac{- sin ( 2 a ) ( sin ( a ) - 1 ) - cos ^{3} ( a )}{( sin ( a ) - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d a} (cos^{2} (a)) = - sin (2 a)

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

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

Simplify

\frac{( - sin ( 2 a ) ) ( sin ( a ) - 1 ) - cos ( a ) cos ^{2} ( a )}{( sin ( a ) - 1 ) ^{2}} : \frac{- sin ( 2 a ) ( sin ( a ) - 1 ) - cos ^{3} ( a )}{( sin ( a ) - 1 ) ^{2}}

= \frac{- sin ( 2 a ) ( sin ( a ) - 1 ) - cos ^{3} ( a )}{( sin ( a ) - 1 ) ^{2}}

t an g e n t f (x) = x^{4} + 4 x^{2} - x, (1, 4)

\int \frac{x ^{2}}{x ^{2} + 16} d x

n = 1 \sum \infty \frac{1000}{5 ^{n}}

l a pl a ce t r an s f or m 5 + 4 e^{- 2 t}

\int (2 x) d x

What is the d/(da)((cos^2(a))/(sin(a)-1)) ?
The d/(da)((cos^2(a))/(sin(a)-1)) is (-sin(2a)(sin(a)-1)-cos^3(a))/((sin(a)-1)^2)
What is the first d/(da)((cos^2(a))/(sin(a)-1)) ?
The first d/(da)((cos^2(a))/(sin(a)-1)) is (-sin(2a)(sin(a)-1)-cos^3(a))/((sin(a)-1)^2)