What is the derivative of f(x)=2xsin(3x) ?

The derivative of f(x)=2xsin(3x) is 2(sin(3x)+3xcos(3x))

What is the first derivative of f(x)=2xsin(3x) ?

The first derivative of f(x)=2xsin(3x) is 2(sin(3x)+3xcos(3x))

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derivative of

f (x) = 2 x sin (3 x)

2 (sin (3 x) + 3 x cos (3 x))

Solution steps

\frac{d}{d x} (2 x sin (3 x))

Take the constant out:

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

= 2 \frac{d}{d x} (x sin (3 x))

Apply the Product Rule:

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

f = x, g = sin (3 x)

= 2 (\frac{d x}{d x} sin (3 x) + \frac{d}{d x} (sin (3 x)) x)

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

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

= 2 (1 \cdot sin (3 x) + cos (3 x) \cdot 3 x)

Simplify

= 2 (sin (3 x) + 3 x cos (3 x))

y = \frac{2 x + 1}{2 x - 1}

3 x - 45 - 15 y = 0

y = \frac{x ^{2} + 4 x + 3}{x}

f (x) = \frac{1 - sec ( x )}{tan ( x )}

x = - 2

What is the derivative of f(x)=2xsin(3x) ?
The derivative of f(x)=2xsin(3x) is 2(sin(3x)+3xcos(3x))
What is the first derivative of f(x)=2xsin(3x) ?
The first derivative of f(x)=2xsin(3x) is 2(sin(3x)+3xcos(3x))