What is the derivative of 4x^6(x^4-3x) ?

The derivative of 4x^6(x^4-3x) is 4(10x^9-21x^6)

What is the first derivative of 4x^6(x^4-3x) ?

The first derivative of 4x^6(x^4-3x) is 4(10x^9-21x^6)

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derivative of

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

4 (10 x^{9} - 21 x^{6})

Solution steps

\frac{d}{d x} (4 x^{6} (x^{4} - 3 x))

Take the constant out:

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

= 4 \frac{d}{d x} (x^{6} (x^{4} - 3 x))

Apply the Product Rule:

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

f = x^{6}, g = x^{4} - 3 x

= 4 (\frac{d}{d x} (x^{6}) (x^{4} - 3 x) + \frac{d}{d x} (x^{4} - 3 x) x^{6})

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 4 (6 x^{5} (x^{4} - 3 x) + (4 x^{3} - 3) x^{6})

Expand

6 x^{5} (x^{4} - 3 x) + (4 x^{3} - 3) x^{6} : 10 x^{9} - 21 x^{6}

= 4 (10 x^{9} - 21 x^{6})

What is the derivative of 4x^6(x^4-3x) ?
The derivative of 4x^6(x^4-3x) is 4(10x^9-21x^6)
What is the first derivative of 4x^6(x^4-3x) ?
The first derivative of 4x^6(x^4-3x) is 4(10x^9-21x^6)