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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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