What is the derivative of 3sin(x+3xcos(x)) ?

The derivative of 3sin(x+3xcos(x)) is 6cos(x)-3xsin(x)

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

The first derivative of 3sin(x+3xcos(x)) is 6cos(x)-3xsin(x)

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

6 cos (x) - 3 x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 3 cos (x) + 3 (cos (x) - x sin (x))

Simplify

3 cos (x) + 3 (cos (x) - x sin (x)) : 6 cos (x) - 3 x sin (x)

= 6 cos (x) - 3 x sin (x)

What is the derivative of 3sin(x+3xcos(x)) ?
The derivative of 3sin(x+3xcos(x)) is 6cos(x)-3xsin(x)
What is the first derivative of 3sin(x+3xcos(x)) ?
The first derivative of 3sin(x+3xcos(x)) is 6cos(x)-3xsin(x)