What is the derivative of (9x^2)(-1+2x) ?

The derivative of (9x^2)(-1+2x) is 9(-2x+6x^2)

What is the first derivative of (9x^2)(-1+2x) ?

The first derivative of (9x^2)(-1+2x) is 9(-2x+6x^2)

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derivative of

(9 x^{2}) (- 1 + 2 x)

9 (- 2 x + 6 x^{2})

Solution steps

\frac{d}{d x} (9 x^{2} (- 1 + 2 x))

Take the constant out:

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

= 9 \frac{d}{d x} (x^{2} (- 1 + 2 x))

Apply the Product Rule:

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

f = x^{2}, g = - 1 + 2 x

= 9 (\frac{d}{d x} (x^{2}) (- 1 + 2 x) + \frac{d}{d x} (- 1 + 2 x) x^{2})

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

\frac{d}{d x} (- 1 + 2 x) = 2

= 9 (2 x (- 1 + 2 x) + 2 x^{2})

Expand

2 x (- 1 + 2 x) + 2 x^{2} : - 2 x + 6 x^{2}

= 9 (- 2 x + 6 x^{2})

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What is the derivative of (9x^2)(-1+2x) ?
The derivative of (9x^2)(-1+2x) is 9(-2x+6x^2)
What is the first derivative of (9x^2)(-1+2x) ?
The first derivative of (9x^2)(-1+2x) is 9(-2x+6x^2)