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

The derivative of (csc(t)+cot(t))^{-1} is (csc(t))/(csc(t)+cot(t))

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

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

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derivative of

(csc (t) + cot (t))^{- 1}

\frac{csc ( t )}{csc ( t ) + cot ( t )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( csc ( t ) + cot ( t ) ) ^{2}} (- cot (t) csc (t) - csc^{2} (t)) : \frac{csc ( t )}{csc ( t ) + cot ( t )}

= \frac{csc ( t )}{csc ( t ) + cot ( t )}

\frac{d}{d x} ((x - 3) e^{x})

x \to 0 lim (\frac{( tan ( x ) )}{x})

\int_{0}^{1} x^{2} - 1 d x

\int (3 x^{4} + x^{5}) d x

(1 + y^{2}) d x + x y d y = 0

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