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Popular >

derivative of cos(x-1/6 cos(3x))

Solution

\frac{d}{d x} (cos (x) - \frac{1}{6} cos (3 x))

Solution

- sin (x) + \frac{1}{2} sin (3 x)

Solution steps

\frac{d}{d x} (cos (x) - \frac{1}{6} cos (3 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (cos (x)) - \frac{d}{d x} (\frac{1}{6} cos (3 x))

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

\frac{d}{d x} (\frac{1}{6} cos (3 x)) = - \frac{1}{2} sin (3 x)

= - sin (x) - (- \frac{1}{2} sin (3 x))

Simplify

= - sin (x) + \frac{1}{2} sin (3 x)

Popular Examples

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\int_{1}^{2} \frac{5 x}{x ^{2} + 1} d x

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

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\frac{1}{60} w h

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\int (x + 1) (x^{2} + 2 x)^{2} d x

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\frac{d}{d x} (\frac{64}{x})

Frequently Asked Questions (FAQ)

What is the derivative of cos(x-1/6 cos(3x)) ?
The derivative of cos(x-1/6 cos(3x)) is -sin(x)+1/2 sin(3x)
What is the first derivative of cos(x-1/6 cos(3x)) ?
The first derivative of cos(x-1/6 cos(3x)) is -sin(x)+1/2 sin(3x)