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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = sin (2 x)

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

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

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

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

Simplify

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

\int \frac{1}{x 6 - x ^{2}} d x

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

θ \to \infty lim (e^{- 3 θ} cos (θ))

h \to 0 lim (\frac{( a ^{u + h} - a ^{u} )}{h})

\int e^{- a x} sin (b x) d x

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