What is the derivative of cos(x-cos(2x)) ?

The derivative of cos(x-cos(2x)) is -sin(x)+2sin(2x)

What is the first derivative of cos(x-cos(2x)) ?

The first derivative of cos(x-cos(2x)) is -sin(x)+2sin(2x)

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\frac{d}{d x} (cos (x) - cos (2 x))

- sin (x) + 2 sin (2 x)

Solution steps

\frac{d}{d x} (cos (x) - cos (2 x))

Apply the Sum/Difference Rule:

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

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

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

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

= - sin (x) - (- sin (2 x) \cdot 2)

Simplify

= - sin (x) + 2 sin (2 x)

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