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

The derivative of f(x)=2x^6(x^4-2x) is 2(10x^9-14x^6)

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

The first derivative of f(x)=2x^6(x^4-2x) is 2(10x^9-14x^6)

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derivative of

f (x) = 2 x^{6} (x^{4} - 2 x)

2 (10 x^{9} - 14 x^{6})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{6}, g = x^{4} - 2 x

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

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

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

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

Expand

6 x^{5} (x^{4} - 2 x) + (4 x^{3} - 2) x^{6} : 10 x^{9} - 14 x^{6}

= 2 (10 x^{9} - 14 x^{6})

\int arctan (7 t) d t

\int_{2}^{\infty} \frac{1}{5 x ^{2}} d x

\frac{1}{1 - x}, 4

x \to 0 lim (6 x^{2})

(x^{2} + 1) y^{^{'}} + 5 x y = 5 x, y (0) = 6

What is the derivative of f(x)=2x^6(x^4-2x) ?
The derivative of f(x)=2x^6(x^4-2x) is 2(10x^9-14x^6)
What is the first derivative of f(x)=2x^6(x^4-2x) ?
The first derivative of f(x)=2x^6(x^4-2x) is 2(10x^9-14x^6)