What is the derivative of cos(3x-sin(3x)) ?

The derivative of cos(3x-sin(3x)) is -sin(3x)*3-cos(3x)*3

What is the first derivative of cos(3x-sin(3x)) ?

The first derivative of cos(3x-sin(3x)) is -sin(3x)*3-cos(3x)*3

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\frac{d}{d x} (cos (3 x) - sin (3 x))

- sin (3 x) \cdot 3 - cos (3 x) \cdot 3

Solution steps

\frac{d}{d x} (cos (3 x) - sin (3 x))

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= - sin (3 x) \cdot 3 - cos (3 x) \cdot 3

f (x) = (x^{5} - x^{3} + 3)^{4}

f (x) = x^{2} + 10

f (p) = 3 p^{2}

f (x) = 3 x + 3

f (x) = 3 x + 5

What is the derivative of cos(3x-sin(3x)) ?
The derivative of cos(3x-sin(3x)) is -sin(3x)*3-cos(3x)*3
What is the first derivative of cos(3x-sin(3x)) ?
The first derivative of cos(3x-sin(3x)) is -sin(3x)*3-cos(3x)*3