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

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

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

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

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

- sin (2 x) \cdot 2 + cos (2 x) \cdot 2

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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