What is the derivative of 4x^2cos(2x) ?

The derivative of 4x^2cos(2x) is 4(2xcos(2x)-2x^2sin(2x))

What is the first derivative of 4x^2cos(2x) ?

The first derivative of 4x^2cos(2x) is 4(2xcos(2x)-2x^2sin(2x))

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\frac{d}{d x} (4 x^{2} cos (2 x))

4 (2 x cos (2 x) - 2 x^{2} sin (2 x))

Solution steps

\frac{d}{d x} (4 x^{2} cos (2 x))

Take the constant out:

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

= 4 \frac{d}{d x} (x^{2} cos (2 x))

Apply the Product Rule:

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

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

= 4 (\frac{d}{d x} (x^{2}) cos (2 x) + \frac{d}{d x} (cos (2 x)) x^{2})

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

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

= 4 (2 x cos (2 x) + (- sin (2 x) \cdot 2) x^{2})

Simplify

= 4 (2 x cos (2 x) - 2 x^{2} sin (2 x))

What is the derivative of 4x^2cos(2x) ?
The derivative of 4x^2cos(2x) is 4(2xcos(2x)-2x^2sin(2x))
What is the first derivative of 4x^2cos(2x) ?
The first derivative of 4x^2cos(2x) is 4(2xcos(2x)-2x^2sin(2x))