What is the derivative of 1/(csc(x+cot(x))) ?

The derivative of 1/(csc(x+cot(x))) is (csc(x))/(csc(x)+cot(x))

What is the first derivative of 1/(csc(x+cot(x))) ?

The first derivative of 1/(csc(x+cot(x))) is (csc(x))/(csc(x)+cot(x))

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

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

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

2 arcsin (x^{3})

\frac{d}{d x} (10 e^{- 2 x})

h (t) = (t + 5)^{\frac{2}{3}} (3 t^{2} - 5)^{3}

x \to 9 lim (\frac{5}{( x - 9 )})

7 y y^{^{'}} = x

What is the derivative of 1/(csc(x+cot(x))) ?
The derivative of 1/(csc(x+cot(x))) is (csc(x))/(csc(x)+cot(x))
What is the first derivative of 1/(csc(x+cot(x))) ?
The first derivative of 1/(csc(x+cot(x))) is (csc(x))/(csc(x)+cot(x))