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Popular >

derivative of (1+cos(2x)^{-4})

Solution

\frac{d}{d x} ((1 + cos (2 x))^{- 4})

Solution

\frac{sin ( 2 x )}{4 cos ^{10} ( x )}

Solution steps

\frac{d}{d x} ((1 + cos (2 x))^{- 4})

Apply the chain rule:

- \frac{4}{( 1 + cos ( 2 x ) ) ^{5}} \frac{d}{d x} (1 + cos (2 x))

= - \frac{4}{( 1 + cos ( 2 x ) ) ^{5}} \frac{d}{d x} (1 + cos (2 x))

\frac{d}{d x} (1 + cos (2 x)) = - 2 sin (2 x)

= - \frac{4}{( 1 + cos ( 2 x ) ) ^{5}} (- 2 sin (2 x))

Simplify

- \frac{4}{( 1 + cos ( 2 x ) ) ^{5}} (- 2 sin (2 x)) : \frac{sin ( 2 x )}{4 cos ^{10} ( x )}

= \frac{sin ( 2 x )}{4 cos ^{10} ( x )}

Popular Examples

derivative of 1/((3+x^2))

\frac{d}{d x} (\frac{1}{( 3 + x ) ^{2}})

integral of e^{6x+7}

\int e^{6 x + 7} d x

tangent of 3/(1+x^2)tangent of

\frac{3}{1 + x ^{2}}

tangent of xy-picos(y)=3pi,(2,pi)tangent of

x y - π cos (y) = 3 π, (2, π)

(\partial}{\partial t}(\frac{2r+s)/t)

\frac{\partial}{\partial t} (\frac{2 r + s}{t})

Frequently Asked Questions (FAQ)

What is the derivative of (1+cos(2x)^{-4}) ?
The derivative of (1+cos(2x)^{-4}) is (sin(2x))/(4cos^{10)(x)}
What is the first derivative of (1+cos(2x)^{-4}) ?
The first derivative of (1+cos(2x)^{-4}) is (sin(2x))/(4cos^{10)(x)}