What is the d/(dθ)((csc(θ)+cot(θ))^{-1}) ?

The d/(dθ)((csc(θ)+cot(θ))^{-1}) is (csc(θ))/(csc(θ)+cot(θ))

What is the first d/(dθ)((csc(θ)+cot(θ))^{-1}) ?

The first d/(dθ)((csc(θ)+cot(θ))^{-1}) is (csc(θ))/(csc(θ)+cot(θ))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} + e^{x + y} = 0

\int \frac{x ^{2}}{( x ^{3} + 5 ) ^{2}} d x

\frac{\partial}{\partial x} (4 x + y^{3})

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

x \to 1 lim (sin (π x))

What is the d/(dθ)((csc(θ)+cot(θ))^{-1}) ?
The d/(dθ)((csc(θ)+cot(θ))^{-1}) is (csc(θ))/(csc(θ)+cot(θ))
What is the first d/(dθ)((csc(θ)+cot(θ))^{-1}) ?
The first d/(dθ)((csc(θ)+cot(θ))^{-1}) is (csc(θ))/(csc(θ)+cot(θ))