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

The -derivative of sin(3x) is -x derivative of sin(3x)+3xcos(3x)-sin(3x)+C

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Find the Derivative - d/dx sin(3x)

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply Integration By Parts

: x \frac{d}{d x} (sin (3 x)) - \int - 9 x sin (3 x) d x

= - (x \frac{d}{d x} (sin (3 x)) - \int - 9 x sin (3 x) d x)

\int - 9 x sin (3 x) d x = 3 x cos (3 x) - sin (3 x)

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

Simplify

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

Add a constant to the solution

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

- \frac{d}{d x} (2 cos (x))

- \frac{d}{d x} (\frac{1}{( 2 x )})

- \frac{d}{d x} y = \frac{5}{x}

- \frac{d}{d x} y = \frac{( sec ( x ) )}{x}

- \frac{d}{d x} (tan (2 x))

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