What is the derivative of csc^7(x) ?

The derivative of csc^7(x) is -7csc^7(x)cot(x)

What is the first derivative of csc^7(x) ?

The first derivative of csc^7(x) is -7csc^7(x)cot(x)

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\frac{d}{d x} (csc^{7} (x))

- 7 csc^{7} (x) cot (x)

Solution steps

\frac{d}{d x} (csc^{7} (x))

Apply the chain rule:

7 (csc (x))^{6} \frac{d}{d x} (csc (x))

= 7 (csc (x))^{6} \frac{d}{d x} (csc (x))

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

= 7 (csc (x))^{6} (- cot (x) csc (x))

Simplify

7 csc^{6} (x) (- cot (x) csc (x)) : - 7 csc^{7} (x) cot (x)

= - 7 csc^{7} (x) cot (x)

\int \frac{x + 2}{( x ^{2} + 2 x + 10 ) ^{\frac{5}{2}}} d x

0 = 2 x + 1 - 2 y y^{^{'}}, y (- 2) = - 1

\frac{d}{d x} (sin (2 \cdot x))

\frac{d}{d x} (5 + cos (x^{2}))

\int e^{5 y} d y

What is the derivative of csc^7(x) ?
The derivative of csc^7(x) is -7csc^7(x)cot(x)
What is the first derivative of csc^7(x) ?
The first derivative of csc^7(x) is -7csc^7(x)cot(x)