What is the derivative of csc^3(x^2) ?

The derivative of csc^3(x^2) is -6xcsc^3(x^2)cot(x^2)

What is the first derivative of csc^3(x^2) ?

The first derivative of csc^3(x^2) is -6xcsc^3(x^2)cot(x^2)

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\frac{d}{d x} (csc^{3} (x^{2}))

- 6 x csc^{3} (x^{2}) cot (x^{2})

Solution steps

\frac{d}{d x} (csc^{3} (x^{2}))

Apply the chain rule:

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

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

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

= 3 (csc (x^{2}))^{2} (- cot (x^{2}) csc (x^{2}) \cdot 2 x)

Simplify

3 csc^{2} (x^{2}) (- cot (x^{2}) csc (x^{2}) \cdot 2 x) : - 6 x csc^{3} (x^{2}) cot (x^{2})

= - 6 x csc^{3} (x^{2}) cot (x^{2})

\frac{d}{d x} ((1 + x^{3})^{2020})

\frac{d}{d x} (4 e^{- x^{2}})

(8, 8), (4, 6)

e^{2 x} + 2 e^{2 x} x

\frac{d y}{d t} + a y = b

What is the derivative of csc^3(x^2) ?
The derivative of csc^3(x^2) is -6xcsc^3(x^2)cot(x^2)
What is the first derivative of csc^3(x^2) ?
The first derivative of csc^3(x^2) is -6xcsc^3(x^2)cot(x^2)