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

The derivative of sin(3x+3xcos(3x)) is 6cos(3x)-9xsin(3x)

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

The first derivative of sin(3x+3xcos(3x)) is 6cos(3x)-9xsin(3x)

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

6 cos (3 x) - 9 x sin (3 x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

cos (3 x) \cdot 3 + 3 (cos (3 x) - 3 x sin (3 x)) : 6 cos (3 x) - 9 x sin (3 x)

= 6 cos (3 x) - 9 x sin (3 x)

\frac{d}{d x} (x - e^{- x})

\int (3 x + 2)^{2.4} d x

\frac{\partial}{\partial x} (x^{6} y - 2 x^{5} y^{2})

- 2 x^{4} + 5 x^{2} - 3 (1)

y = e^{t}

What is the derivative of sin(3x+3xcos(3x)) ?
The derivative of sin(3x+3xcos(3x)) is 6cos(3x)-9xsin(3x)
What is the first derivative of sin(3x+3xcos(3x)) ?
The first derivative of sin(3x+3xcos(3x)) is 6cos(3x)-9xsin(3x)