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

The derivative of (3x^4(4x^3+4x)) is 3(28x^6+20x^4)

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

The first derivative of (3x^4(4x^3+4x)) is 3(28x^6+20x^4)

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

3 (28 x^{6} + 20 x^{4})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{4}, g = 4 x^{3} + 4 x

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

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

\frac{d}{d x} (4 x^{3} + 4 x) = 12 x^{2} + 4

= 3 (4 x^{3} (4 x^{3} + 4 x) + (12 x^{2} + 4) x^{4})

Expand

4 x^{3} (4 x^{3} + 4 x) + (12 x^{2} + 4) x^{4} : 28 x^{6} + 20 x^{4}

= 3 (28 x^{6} + 20 x^{4})

What is the derivative of (3x^4(4x^3+4x)) ?
The derivative of (3x^4(4x^3+4x)) is 3(28x^6+20x^4)
What is the first derivative of (3x^4(4x^3+4x)) ?
The first derivative of (3x^4(4x^3+4x)) is 3(28x^6+20x^4)