What is the derivative of f(x)=6x^5(x^3-6x) ?

The derivative of f(x)=6x^5(x^3-6x) is 6(8x^7-36x^5)

What is the first derivative of f(x)=6x^5(x^3-6x) ?

The first derivative of f(x)=6x^5(x^3-6x) is 6(8x^7-36x^5)

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derivative of

f (x) = 6 x^{5} (x^{3} - 6 x)

6 (8 x^{7} - 36 x^{5})

Solution steps

\frac{d}{d x} (6 x^{5} (x^{3} - 6 x))

Take the constant out:

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

= 6 \frac{d}{d x} (x^{5} (x^{3} - 6 x))

Apply the Product Rule:

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

f = x^{5}, g = x^{3} - 6 x

= 6 (\frac{d}{d x} (x^{5}) (x^{3} - 6 x) + \frac{d}{d x} (x^{3} - 6 x) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (x^{3} - 6 x) = 3 x^{2} - 6

= 6 (5 x^{4} (x^{3} - 6 x) + (3 x^{2} - 6) x^{5})

Expand

5 x^{4} (x^{3} - 6 x) + (3 x^{2} - 6) x^{5} : 8 x^{7} - 36 x^{5}

= 6 (8 x^{7} - 36 x^{5})

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What is the derivative of f(x)=6x^5(x^3-6x) ?
The derivative of f(x)=6x^5(x^3-6x) is 6(8x^7-36x^5)
What is the first derivative of f(x)=6x^5(x^3-6x) ?
The first derivative of f(x)=6x^5(x^3-6x) is 6(8x^7-36x^5)