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

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

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

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

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derivative

3 (sin^{2} (x) + x sin (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)) = sin (2 x)

= 3 (1 \cdot sin^{2} (x) + sin (2 x) x)

Simplify

= 3 (sin^{2} (x) + x sin (2 x))

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