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

The derivative of csc^2(2x-csc(2x^2)) is -4csc^2(2x)cot(2x)+4xcot(2x^2)csc(2x^2)

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

The first derivative of csc^2(2x-csc(2x^2)) is -4csc^2(2x)cot(2x)+4xcot(2x^2)csc(2x^2)

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

- 4 csc^{2} (2 x) cot (2 x) + 4 x cot (2 x^{2}) csc (2 x^{2})

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (csc^{2} (2 x)) = - 4 csc^{2} (2 x) cot (2 x)

\frac{d}{d x} (csc (2 x^{2})) = - cot (2 x^{2}) csc (2 x^{2}) \cdot 4 x

= - 4 csc^{2} (2 x) cot (2 x) - (- cot (2 x^{2}) csc (2 x^{2}) \cdot 4 x)

Simplify

= - 4 csc^{2} (2 x) cot (2 x) + 4 x cot (2 x^{2}) csc (2 x^{2})

x \to 7 lim (\frac{x ^{2}}{x} - \frac{49}{7})

y = 4 x - 6 x^{3} + \frac{4}{x}

\frac{d y}{d x} + \frac{y}{x} = x

0.1 (0.7 n^{2} + 9 n + 29)^{(\frac{1}{2})}

\frac{d}{d x} (\frac{5}{x})

What is the derivative of csc^2(2x-csc(2x^2)) ?
The derivative of csc^2(2x-csc(2x^2)) is -4csc^2(2x)cot(2x)+4xcot(2x^2)csc(2x^2)
What is the first derivative of csc^2(2x-csc(2x^2)) ?
The first derivative of csc^2(2x-csc(2x^2)) is -4csc^2(2x)cot(2x)+4xcot(2x^2)csc(2x^2)