What is the derivative of csc^4(x) ?

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

What is the first derivative of csc^4(x) ?

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

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\frac{d}{d x} (csc^{4} (x))

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

Solution steps

\frac{d}{d x} (csc^{4} (x))

Apply the chain rule:

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

= 4 (csc (x))^{3} \frac{d}{d x} (csc (x))

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

= 4 (csc (x))^{3} (- cot (x) csc (x))

Simplify

4 csc^{3} (x) (- cot (x) csc (x)) : - 4 csc^{4} (x) cot (x)

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

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

n = 0 \sum \infty \frac{5}{n !}

\frac{d}{d x} (\frac{1}{x ^{2} + 9})

(3, - 6), (5, - 5)

y = x^{3} - 1, y = x - 1

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