What is the derivative of 2x^2(3x^4-2) ?

The derivative of 2x^2(3x^4-2) is 2(18x^5-4x)

What is the first derivative of 2x^2(3x^4-2) ?

The first derivative of 2x^2(3x^4-2) is 2(18x^5-4x)

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derivative of

2 x^{2} (3 x^{4} - 2)

2 (18 x^{5} - 4 x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = 3 x^{4} - 2

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

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

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

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

Simplify

2 (2 x (3 x^{4} - 2) + 12 x^{3} x^{2}) : 2 (18 x^{5} - 4 x)

= 2 (18 x^{5} - 4 x)

\frac{\partial}{\partial x} (6 x sin (x^{2} y))

y = (x - 2)^{\frac{2}{3}}, (3, 1)

\int e^{- \frac{1}{3} x} d x

\frac{d}{d x} (cot (e^{x}))

\int \frac{x + 4}{x ^{2} + 6 x + 18} d x

What is the derivative of 2x^2(3x^4-2) ?
The derivative of 2x^2(3x^4-2) is 2(18x^5-4x)
What is the first derivative of 2x^2(3x^4-2) ?
The first derivative of 2x^2(3x^4-2) is 2(18x^5-4x)