What is the derivative of 2/(cos(xcot(x))) ?

The derivative of 2/(cos(xcot(x))) is -(2(-cos(x)-cot(x)csc(x)))/(cos^2(x)cot^2(x))

What is the first derivative of 2/(cos(xcot(x))) ?

The first derivative of 2/(cos(xcot(x))) is -(2(-cos(x)-cot(x)csc(x)))/(cos^2(x)cot^2(x))

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\frac{d}{d x} (\frac{2}{cos ( x ) cot ( x )})

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

Solution steps

\frac{d}{d x} (\frac{2}{cos ( x ) cot ( x )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{1}{( cos ( x ) cot ( x ) ) ^{2}} \frac{d}{d x} (cos (x) cot (x))

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

\frac{d}{d x} (cos (x) cot (x)) = - cos (x) - cot (x) csc (x)

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

Simplify

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

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

\int \frac{5}{x + 6} d x

y = x - 4, y^{2} = 2 x

x \to + 0 lim (x ln (\frac{1}{x}))

(sin (x)) (sec (x))

\int_{- 1}^{1} \frac{1}{2} (1 - x^{4}) d x

What is the derivative of 2/(cos(xcot(x))) ?
The derivative of 2/(cos(xcot(x))) is -(2(-cos(x)-cot(x)csc(x)))/(cos^2(x)cot^2(x))
What is the first derivative of 2/(cos(xcot(x))) ?
The first derivative of 2/(cos(xcot(x))) is -(2(-cos(x)-cot(x)csc(x)))/(cos^2(x)cot^2(x))