What is the derivative of x^2cos(4x+3) ?

The derivative of x^2cos(4x+3) is 2xcos(4x+3)-4x^2sin(4x+3)

What is the first derivative of x^2cos(4x+3) ?

The first derivative of x^2cos(4x+3) is 2xcos(4x+3)-4x^2sin(4x+3)

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\frac{d}{d x} (x^{2} cos (4 x + 3))

2 x cos (4 x + 3) - 4 x^{2} sin (4 x + 3)

Solution steps

\frac{d}{d x} (x^{2} cos (4 x + 3))

Apply the Product Rule:

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

f = x^{2}, g = cos (4 x + 3)

= \frac{d}{d x} (x^{2}) cos (4 x + 3) + \frac{d}{d x} (cos (4 x + 3)) x^{2}

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

\frac{d}{d x} (cos (4 x + 3)) = - sin (4 x + 3) \cdot 4

= 2 x cos (4 x + 3) + (- sin (4 x + 3) \cdot 4) x^{2}

Simplify

= 2 x cos (4 x + 3) - 4 x^{2} sin (4 x + 3)

What is the derivative of x^2cos(4x+3) ?
The derivative of x^2cos(4x+3) is 2xcos(4x+3)-4x^2sin(4x+3)
What is the first derivative of x^2cos(4x+3) ?
The first derivative of x^2cos(4x+3) is 2xcos(4x+3)-4x^2sin(4x+3)