What is the d/(du)(sqrt(cos(c)(cot(u)))) ?

The d/(du)(sqrt(cos(c)(cot(u)))) is -(csc^2(u)sqrt(cos(c)))/(2sqrt(cot(u)))

What is the first d/(du)(sqrt(cos(c)(cot(u)))) ?

The first d/(du)(sqrt(cos(c)(cot(u)))) is -(csc^2(u)sqrt(cos(c)))/(2sqrt(cot(u)))

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עברית

العربية

\frac{d}{d u} (cos (c) (cot (u)))

- \frac{csc ^{2} ( u ) cos ( c )}{2 cot ( u )}

Solution steps

\frac{d}{d u} (cos (c) (cot (u)))

Apply the chain rule:

\frac{1}{2 cos ( c ) cot ( u )} \frac{d}{d u} (cos (c) cot (u))

= \frac{1}{2 cos ( c ) cot ( u )} \frac{d}{d u} (cos (c) cot (u))

\frac{d}{d u} (cos (c) cot (u)) = - cos (c) csc^{2} (u)

= \frac{1}{2 cos ( c ) cot ( u )} (- cos (c) csc^{2} (u))

Simplify

\frac{1}{2 cos ( c ) cot ( u )} (- cos (c) csc^{2} (u)) : - \frac{csc ^{2} ( u ) cos ( c )}{2 cot ( u )}

= - \frac{csc ^{2} ( u ) cos ( c )}{2 cot ( u )}

What is the d/(du)(sqrt(cos(c)(cot(u)))) ?
The d/(du)(sqrt(cos(c)(cot(u)))) is -(csc^2(u)sqrt(cos(c)))/(2sqrt(cot(u)))
What is the first d/(du)(sqrt(cos(c)(cot(u)))) ?
The first d/(du)(sqrt(cos(c)(cot(u)))) is -(csc^2(u)sqrt(cos(c)))/(2sqrt(cot(u)))