What is the derivative of g(x)=x^2(1-2x) ?

The derivative of g(x)=x^2(1-2x) is 2x-6x^2

What is the first derivative of g(x)=x^2(1-2x) ?

The first derivative of g(x)=x^2(1-2x) is 2x-6x^2

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derivative of

g (x) = x^{2} (1 - 2 x)

2 x - 6 x^{2}

Solution steps

\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

= \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

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

Simplify

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

= 2 x - 6 x^{2}

\frac{\partial}{\partial x} (x - y)

\frac{d}{d x} (sin (7 x + 2))

\int e^{2 x} sin (e^{x}) d x

\frac{\partial}{\partial x} (- cos (x y))

\int \frac{1}{v} d v

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