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

The derivative of y=2x^2(3x-4) is 2(9x^2-8x)

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

The first derivative of y=2x^2(3x-4) is 2(9x^2-8x)

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derivative of

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

2 (9 x^{2} - 8 x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Expand

2 x (3 x - 4) + 3 x^{2} : 9 x^{2} - 8 x

= 2 (9 x^{2} - 8 x)

(- 1, \frac{π}{3})

y = 5^{x}

(- 36) (6.1)

f (x) = \frac{x}{2}

y = 1

What is the derivative of y=2x^2(3x-4) ?
The derivative of y=2x^2(3x-4) is 2(9x^2-8x)
What is the first derivative of y=2x^2(3x-4) ?
The first derivative of y=2x^2(3x-4) is 2(9x^2-8x)