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

The derivative of 1/(2sin^2(x)) is -(cos(x))/(sin^3(x))

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

The first derivative of 1/(2sin^2(x)) is -(cos(x))/(sin^3(x))

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derivative of

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

- \frac{cos ( x )}{sin ^{3} ( x )}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{2}{( sin ( x ) ) ^{3}} \frac{d}{d x} (sin (x))

= - \frac{2}{( sin ( x ) ) ^{3}} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{1}{2} (- \frac{2}{( sin ( x ) ) ^{3}} cos (x))

Simplify

\frac{1}{2} (- \frac{2}{sin ^{3} ( x )} cos (x)) : - \frac{cos ( x )}{sin ^{3} ( x )}

= - \frac{cos ( x )}{sin ^{3} ( x )}

x^{3} ln^{4} (x)

(1 + x)^{\frac{1}{x}}

5 x + 2

\frac{2 ^{x}}{3 ^{x}}

\frac{( x + 1 )}{( x + 2 ) ^{2}}

What is the derivative of 1/(2sin^2(x)) ?
The derivative of 1/(2sin^2(x)) is -(cos(x))/(sin^3(x))
What is the first derivative of 1/(2sin^2(x)) ?
The first derivative of 1/(2sin^2(x)) is -(cos(x))/(sin^3(x))