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

The -derivative of 3cos(x) is -x derivative of 3cos(x)-3xsin(x)-3cos(x)+C

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

- \frac{d}{d x} (5 e^{x})

- \frac{d}{d x} (e^{t a n (2 x)})

y = \frac{1}{3 x - 4}

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

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

What is the -derivative of 3cos(x) ?
The -derivative of 3cos(x) is -x derivative of 3cos(x)-3xsin(x)-3cos(x)+C