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Popular >

derivative of g(x)=x^2(1-4x)

Solution

derivative of

g (x) = x^{2} (1 - 4 x)

Solution

2 x - 12 x^{2}

Solution steps

\frac{d}{d x} (x^{2} (1 - 4 x))

Apply the Product Rule:

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

f = x^{2}, g = 1 - 4 x

= \frac{d}{d x} (x^{2}) (1 - 4 x) + \frac{d}{d x} (1 - 4 x) x^{2}

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

\frac{d}{d x} (1 - 4 x) = - 4

= 2 x (1 - 4 x) + (- 4) x^{2}

Simplify

2 x (1 - 4 x) + (- 4) x^{2} : 2 x - 12 x^{2}

= 2 x - 12 x^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of g(x)=x^2(1-4x) ?
The derivative of g(x)=x^2(1-4x) is 2x-12x^2
What is the first derivative of g(x)=x^2(1-4x) ?
The first derivative of g(x)=x^2(1-4x) is 2x-12x^2