What is the derivative of csc^{13}(x) ?

The derivative of csc^{13}(x) is -13csc^{13}(x)cot(x)

What is the first derivative of csc^{13}(x) ?

The first derivative of csc^{13}(x) is -13csc^{13}(x)cot(x)

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\frac{d}{d x} (csc^{13} (x))

- 13 csc^{13} (x) cot (x)

Solution steps

\frac{d}{d x} (csc^{13} (x))

Apply the chain rule:

13 (csc (x))^{12} \frac{d}{d x} (csc (x))

= 13 (csc (x))^{12} \frac{d}{d x} (csc (x))

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

= 13 (csc (x))^{12} (- cot (x) csc (x))

Simplify

13 csc^{12} (x) (- cot (x) csc (x)) : - 13 csc^{13} (x) cot (x)

= - 13 csc^{13} (x) cot (x)

x \to \frac{2}{3} lim (\frac{27 x ^{3} - 8}{9 x ^{2} - 4})

t y^{^{'''}} - y^{^{''}} = 0

8 - x

f (x) = \frac{cos ( x )}{x ^{3}}

x \to 5 lim (2 x^{2} - 7 x + 13)

What is the derivative of csc^{13}(x) ?
The derivative of csc^{13}(x) is -13csc^{13}(x)cot(x)
What is the first derivative of csc^{13}(x) ?
The first derivative of csc^{13}(x) is -13csc^{13}(x)cot(x)