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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

y^{^{''}} - 4 y^{^{'}} + 4 y = x e^{2 x}

\frac{d}{d x} ((1 + x + x^{2})^{99})

\frac{\partial}{\partial u} ((u^{2} + v^{2})^{\frac{3}{2}})

x \to 4 - lim (\frac{1}{x - 4})

\int (x^{2} - 1)^{- 1} d x

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