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

The derivative of 2x^2cos(6x) is 2(2xcos(6x)-6x^2sin(6x))

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

The first derivative of 2x^2cos(6x) is 2(2xcos(6x)-6x^2sin(6x))

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

2 (2 x cos (6 x) - 6 x^{2} sin (6 x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= 2 (2 x cos (6 x) - 6 x^{2} sin (6 x))

What is the derivative of 2x^2cos(6x) ?
The derivative of 2x^2cos(6x) is 2(2xcos(6x)-6x^2sin(6x))
What is the first derivative of 2x^2cos(6x) ?
The first derivative of 2x^2cos(6x) is 2(2xcos(6x)-6x^2sin(6x))