What is the derivative of (-1)/(sin^2(x)) ?

The derivative of (-1)/(sin^2(x)) is 2csc^2(x)cot(x)

What is the first derivative of (-1)/(sin^2(x)) ?

The first derivative of (-1)/(sin^2(x)) is 2csc^2(x)cot(x)

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derivative of

\frac{- 1}{sin ^{2} ( x )}

2 csc^{2} (x) cot (x)

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the chain rule:

2 csc (x) \frac{d}{d x} (csc (x))

= 2 csc (x) \frac{d}{d x} (csc (x))

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

= - 2 csc (x) (- cot (x) csc (x))

Simplify

- 2 csc (x) (- cot (x) csc (x)) : 2 csc^{2} (x) cot (x)

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

\frac{d}{d v} (\frac{( v - 0 )}{t})

f (x) = 2 e^{2 x - 3}

lo g_{10} (\frac{2}{( 2 x + 2 )})

x + 6

f (x) = 7 x^{2} + 3 x - 2

What is the derivative of (-1)/(sin^2(x)) ?
The derivative of (-1)/(sin^2(x)) is 2csc^2(x)cot(x)
What is the first derivative of (-1)/(sin^2(x)) ?
The first derivative of (-1)/(sin^2(x)) is 2csc^2(x)cot(x)