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

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

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

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

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

\frac{1}{1 + cos ( a )} - cos (a)

Solution steps

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

Simplify

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cot (a), g = - 1 + cos (a)

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

\frac{d}{d a} (cot (a)) = - csc^{2} (a)

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

= (- csc^{2} (a)) (- 1 + cos (a)) + (- sin (a)) cot (a)

Simplify

(- csc^{2} (a)) (- 1 + cos (a)) + (- sin (a)) cot (a) : \frac{1}{1 + cos ( a )} - cos (a)

= \frac{1}{1 + cos ( a )} - cos (a)

e^{2 x^{2} + 3 x y}

sec^{2} (2 x + 1)

\frac{2}{3} \frac{x ^{4}}{6} + 5 \frac{x ^{4}}{5}

e^{l} o gx + 1

y = (2 t - 3)^{2}

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