What is the derivative of f(x)=4x^{(2)}(x-3) ?

The derivative of f(x)=4x^{(2)}(x-3) is 4(3x^2-6x)

What is the first derivative of f(x)=4x^{(2)}(x-3) ?

The first derivative of f(x)=4x^{(2)}(x-3) is 4(3x^2-6x)

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derivative of

f (x) = 4 x^{(2)} (x - 3)

4 (3 x^{2} - 6 x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = x - 3

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

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

\frac{d}{d x} (x - 3) = 1

= 4 (2 x (x - 3) + 1 \cdot x^{2})

Simplify

4 (2 x (x - 3) + 1 \cdot x^{2}) : 4 (3 x^{2} - 6 x)

= 4 (3 x^{2} - 6 x)

x \to \infty lim (x^{2} + 2 x)

\frac{d}{d x} (arctan (\frac{8}{x}))

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

\frac{\partial}{\partial y} (x^{3} y^{10} sin (x y^{2}))

\int 6 t e^{3 t} d t

What is the derivative of f(x)=4x^{(2)}(x-3) ?
The derivative of f(x)=4x^{(2)}(x-3) is 4(3x^2-6x)
What is the first derivative of f(x)=4x^{(2)}(x-3) ?
The first derivative of f(x)=4x^{(2)}(x-3) is 4(3x^2-6x)