What is the derivative of (3+csc(2t))^{-6} ?

The derivative of (3+csc(2t))^{-6} is (12cot(2t)csc(2t))/((3+csc(2t))^7)

What is the first derivative of (3+csc(2t))^{-6} ?

The first derivative of (3+csc(2t))^{-6} is (12cot(2t)csc(2t))/((3+csc(2t))^7)

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derivative of

(3 + csc (2 t))^{- 6}

\frac{12 cot ( 2 t ) csc ( 2 t )}{( 3 + csc ( 2 t ) ) ^{7}}

Solution steps

\frac{d}{d t} ((3 + csc (2 t))^{- 6})

Apply the chain rule:

- \frac{6}{( 3 + csc ( 2 t ) ) ^{7}} \frac{d}{d t} (3 + csc (2 t))

= - \frac{6}{( 3 + csc ( 2 t ) ) ^{7}} \frac{d}{d t} (3 + csc (2 t))

\frac{d}{d t} (3 + csc (2 t)) = - 2 cot (2 t) csc (2 t)

= - \frac{6}{( 3 + csc ( 2 t ) ) ^{7}} (- 2 cot (2 t) csc (2 t))

Simplify

- \frac{6}{( 3 + csc ( 2 t ) ) ^{7}} (- 2 cot (2 t) csc (2 t)) : \frac{12 cot ( 2 t ) csc ( 2 t )}{( 3 + csc ( 2 t ) ) ^{7}}

= \frac{12 cot ( 2 t ) csc ( 2 t )}{( 3 + csc ( 2 t ) ) ^{7}}

f (x) = - 2 - cos (x), at x = - \frac{π}{4}

\frac{1}{( s - 1 )}

f (x) = x^{2} - 7, (2, - 3)

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

y = 9 x, y = x^{2} - 10, y = 0

What is the derivative of (3+csc(2t))^{-6} ?
The derivative of (3+csc(2t))^{-6} is (12cot(2t)csc(2t))/((3+csc(2t))^7)
What is the first derivative of (3+csc(2t))^{-6} ?
The first derivative of (3+csc(2t))^{-6} is (12cot(2t)csc(2t))/((3+csc(2t))^7)