What is the derivative of (x3x(x+4)^2) ?

The derivative of (x3x(x+4)^2) is 3(4x^3+24x^2+32x)

What is the first derivative of (x3x(x+4)^2) ?

The first derivative of (x3x(x+4)^2) is 3(4x^3+24x^2+32x)

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

3 (4 x^{3} + 24 x^{2} + 32 x)

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

= 3 (2 x (x + 4)^{2} + 2 (x + 4) x^{2})

Expand

2 x (x + 4)^{2} + 2 (x + 4) x^{2} : 4 x^{3} + 24 x^{2} + 32 x

= 3 (4 x^{3} + 24 x^{2} + 32 x)

\frac{2 ( s + 2 )}{s ^{2} + 4 s + 3}

- \frac{4}{( x + 1 ) ^{2}}

2 x e^{x} + e^{x} (x^{2} - 1)

90 - 12

x (a x e^{(- b x)} - 1)

What is the derivative of (x3x(x+4)^2) ?
The derivative of (x3x(x+4)^2) is 3(4x^3+24x^2+32x)
What is the first derivative of (x3x(x+4)^2) ?
The first derivative of (x3x(x+4)^2) is 3(4x^3+24x^2+32x)