What is the derivative of x^2sin(6x) ?

The derivative of x^2sin(6x) is 2xsin(6x)+cos(6x)*6x^2

What is the first derivative of x^2sin(6x) ?

The first derivative of x^2sin(6x) is 2xsin(6x)+cos(6x)*6x^2

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\frac{d}{d x} (x^{2} sin (6 x))

2 x sin (6 x) + cos (6 x) \cdot 6 x^{2}

Solution steps

\frac{d}{d x} (x^{2} sin (6 x))

Apply the Product Rule:

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

f = x^{2}, g = sin (6 x)

= \frac{d}{d x} (x^{2}) sin (6 x) + \frac{d}{d x} (sin (6 x)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

= 2 x sin (6 x) + cos (6 x) \cdot 6 x^{2}

What is the derivative of x^2sin(6x) ?
The derivative of x^2sin(6x) is 2xsin(6x)+cos(6x)*6x^2
What is the first derivative of x^2sin(6x) ?
The first derivative of x^2sin(6x) is 2xsin(6x)+cos(6x)*6x^2