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Popular Calculus >

derivative of f(x)=x^2(1-8x)

Solution

derivative of

f (x) = x^{2} (1 - 8 x)

Solution

2 x - 24 x^{2}

Solution steps

\frac{d}{d x} (x^{2} (1 - 8 x))

Apply the Product Rule:

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

f = x^{2}, g = 1 - 8 x

= \frac{d}{d x} (x^{2}) (1 - 8 x) + \frac{d}{d x} (1 - 8 x) x^{2}

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

\frac{d}{d x} (1 - 8 x) = - 8

= 2 x (1 - 8 x) + (- 8) x^{2}

Simplify

2 x (1 - 8 x) + (- 8) x^{2} : 2 x - 24 x^{2}

= 2 x - 24 x^{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^2(1-8x) ?
The derivative of f(x)=x^2(1-8x) is 2x-24x^2
What is the first derivative of f(x)=x^2(1-8x) ?
The first derivative of f(x)=x^2(1-8x) is 2x-24x^2