What is the derivative of (csc(x)-cot(x))^{-1} ?

The derivative of (csc(x)-cot(x))^{-1} is -1/((csc(x)-cot(x))^2(1+cos(x)))

What is the first derivative of (csc(x)-cot(x))^{-1} ?

The first derivative of (csc(x)-cot(x))^{-1} is -1/((csc(x)-cot(x))^2(1+cos(x)))

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derivative of

(csc (x) - cot (x))^{- 1}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = \frac{1}{x ^{4}}, (1, 1)

\int sinh (9 x) d x

\int \frac{ln ( 18 x )}{x} d x

x \to \frac{π}{3} lim (cos (x) + 2)

\frac{d y}{d x} = \frac{x ^{3} x ^{4} - 1}{y ^{3}}

What is the derivative of (csc(x)-cot(x))^{-1} ?
The derivative of (csc(x)-cot(x))^{-1} is -1/((csc(x)-cot(x))^2(1+cos(x)))
What is the first derivative of (csc(x)-cot(x))^{-1} ?
The first derivative of (csc(x)-cot(x))^{-1} is -1/((csc(x)-cot(x))^2(1+cos(x)))