Solution of \frac{d}{dx} \left( -\csc^2(x) \right)

2\csc^{3}\left(x\right)\cos\left(x\right)

Solve fracddx ( -csc^2(x) )

Evaluate

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

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

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

Use the chain rule \frac{d}{d x} (f (g)) = \frac{d}{d g} (f (g)) \times \frac{d}{d x} (g) where the g = csc (x), to find the derivative

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

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

- 2 g \times \frac{d}{d x} (csc (x))

Use \frac{d}{d x} (csc x) = - csc x cot x to find derivative

- 2 g (- csc (x) cot (x))

Substitute back

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

Rewrite the expression

2 csc (x) csc (x) cot (x)

Calculate

More Steps

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

Calculate

More Steps

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

Calculate

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

Calculate

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

Rewrite the expression

2 sin^{- 3} (x) cos (x)

Rewrite the expression

2 cos (x) sin^{- 3} (x)

Simplify

2 cos (x) csc^{3} (x)

Solution

2 csc^{3} (x) cos (x)