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

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

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

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

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

sin (2 x)

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

= 2 sin (x) cos (x)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= sin (2 x)

\int \frac{1}{2 x ^{2} + 8 x + 25} d x

\frac{d y}{d x} = - \frac{5 x}{y}

\frac{d}{d x} (e^{t a n (2 x + 1)})

x \to 5 - lim (∣ x - 5 ∣)

\int - cos (x) + sin (x) + 2 d x

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