What is the -derivative of sin(2x) ?

The -derivative of sin(2x) is -x derivative of sin(2x)+2xcos(2x)-sin(2x)+C

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Find the Derivative - d/dx sin(2x)

\int - \frac{d}{d x} (sin (2 x)) d x

- x \frac{d}{d x} (sin (2 x)) + 2 x cos (2 x) - sin (2 x) + C

Solution steps

\int - \frac{d}{d x} (sin (2 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 (2 x)) d x

Apply Integration By Parts

: x \frac{d}{d x} (sin (2 x)) - \int - 4 x sin (2 x) d x

= - (x \frac{d}{d x} (sin (2 x)) - \int - 4 x sin (2 x) d x)

\int - 4 x sin (2 x) d x = 2 x cos (2 x) - sin (2 x)

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

Simplify

= - x \frac{d}{d x} (sin (2 x)) + 2 x cos (2 x) - sin (2 x)

Add a constant to the solution

= - x \frac{d}{d x} (sin (2 x)) + 2 x cos (2 x) - sin (2 x) + C

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

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

(- 4, 2), (4, - 4)

- \frac{d}{d x} (sin (x^{2}))

\int (e^{x y}) d x

What is the -derivative of sin(2x) ?
The -derivative of sin(2x) is -x derivative of sin(2x)+2xcos(2x)-sin(2x)+C