What is the derivative of 4x*sin(x) ?

The derivative of 4x*sin(x) is 4(sin(x)+xcos(x))

What is the first derivative of 4x*sin(x) ?

The first derivative of 4x*sin(x) is 4(sin(x)+xcos(x))

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\frac{d}{d x} (4 x \cdot sin (x))

4 (sin (x) + x cos (x))

Solution steps

\frac{d}{d x} (4 x sin (x))

Take the constant out:

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

= 4 \frac{d}{d x} (x sin (x))

Apply the Product Rule:

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

f = x, g = sin (x)

= 4 (\frac{d x}{d x} sin (x) + \frac{d}{d x} (sin (x)) x)

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

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

= 4 (1 \cdot sin (x) + cos (x) x)

Simplify

= 4 (sin (x) + x cos (x))

What is the derivative of 4x*sin(x) ?
The derivative of 4x*sin(x) is 4(sin(x)+xcos(x))
What is the first derivative of 4x*sin(x) ?
The first derivative of 4x*sin(x) is 4(sin(x)+xcos(x))