What is the derivative of 6x^4(x^2-7x) ?

The derivative of 6x^4(x^2-7x) is 6(6x^5-35x^4)

What is the first derivative of 6x^4(x^2-7x) ?

The first derivative of 6x^4(x^2-7x) is 6(6x^5-35x^4)

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\frac{d}{d x} (6 x^{4} (x^{2} - 7 x))

6 (6 x^{5} - 35 x^{4})

Solution steps

\frac{d}{d x} (6 x^{4} (x^{2} - 7 x))

Take the constant out:

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

= 6 \frac{d}{d x} (x^{4} (x^{2} - 7 x))

Apply the Product Rule:

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

f = x^{4}, g = x^{2} - 7 x

= 6 (\frac{d}{d x} (x^{4}) (x^{2} - 7 x) + \frac{d}{d x} (x^{2} - 7 x) x^{4})

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

\frac{d}{d x} (x^{2} - 7 x) = 2 x - 7

= 6 (4 x^{3} (x^{2} - 7 x) + (2 x - 7) x^{4})

Expand

4 x^{3} (x^{2} - 7 x) + (2 x - 7) x^{4} : 6 x^{5} - 35 x^{4}

= 6 (6 x^{5} - 35 x^{4})

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What is the derivative of 6x^4(x^2-7x) ?
The derivative of 6x^4(x^2-7x) is 6(6x^5-35x^4)
What is the first derivative of 6x^4(x^2-7x) ?
The first derivative of 6x^4(x^2-7x) is 6(6x^5-35x^4)