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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (3 x)

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

\frac{d x}{d x} = 1

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

= - (1 \cdot cos (3 x) + (- sin (3 x) \cdot 3) x)

Simplify

- (1 \cdot cos (3 x) + (- sin (3 x) \cdot 3) x) : - cos (3 x) + 3 x sin (3 x)

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

\frac{d}{d x} (arcsin (3 x + 1))

\int \frac{2}{x ^{3} x ^{4} - 25} d x

\int \frac{1}{x ^{3} x ^{2} - 4} d x

\int 9 x^{2} - 30 x + 15 d x

\frac{\partial}{\partial x} (x \cdot sin (y - z))

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