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Popular >

derivative of (1+cos(5t))^{-4}

Solution

derivative of

(1 + cos (5 t))^{- 4}

Solution

\frac{20 sin ( 5 t )}{( 1 + cos ( 5 t ) ) ^{5}}

Solution steps

\frac{d}{d t} ((1 + cos (5 t))^{- 4})

Apply the chain rule:

- \frac{4}{( 1 + cos ( 5 t ) ) ^{5}} \frac{d}{d t} (1 + cos (5 t))

= - \frac{4}{( 1 + cos ( 5 t ) ) ^{5}} \frac{d}{d t} (1 + cos (5 t))

\frac{d}{d t} (1 + cos (5 t)) = - 5 sin (5 t)

= - \frac{4}{( 1 + cos ( 5 t ) ) ^{5}} (- 5 sin (5 t))

Simplify

- \frac{4}{( 1 + cos ( 5 t ) ) ^{5}} (- 5 sin (5 t)) : \frac{20 sin ( 5 t )}{( 1 + cos ( 5 t ) ) ^{5}}

= \frac{20 sin ( 5 t )}{( 1 + cos ( 5 t ) ) ^{5}}

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\int \frac{- 5 e ^{- 5 x}}{( e ^{- 5 x} + 3 ) ^{3}} d x

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Frequently Asked Questions (FAQ)

What is the derivative of (1+cos(5t))^{-4} ?
The derivative of (1+cos(5t))^{-4} is (20sin(5t))/((1+cos(5t))^5)
What is the first derivative of (1+cos(5t))^{-4} ?
The first derivative of (1+cos(5t))^{-4} is (20sin(5t))/((1+cos(5t))^5)