What is the derivative of f(x)=x^2(1-5x) ?

The derivative of f(x)=x^2(1-5x) is 2x-15x^2

What is the first derivative of f(x)=x^2(1-5x) ?

The first derivative of f(x)=x^2(1-5x) is 2x-15x^2

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derivative of

f (x) = x^{2} (1 - 5 x)

2 x - 15 x^{2}

Solution steps

\frac{d}{d x} (x^{2} (1 - 5 x))

Apply the Product Rule:

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

f = x^{2}, g = 1 - 5 x

= \frac{d}{d x} (x^{2}) (1 - 5 x) + \frac{d}{d x} (1 - 5 x) x^{2}

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

\frac{d}{d x} (1 - 5 x) = - 5

= 2 x (1 - 5 x) + (- 5) x^{2}

Simplify

2 x (1 - 5 x) + (- 5) x^{2} : 2 x - 15 x^{2}

= 2 x - 15 x^{2}

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What is the derivative of f(x)=x^2(1-5x) ?
The derivative of f(x)=x^2(1-5x) is 2x-15x^2
What is the first derivative of f(x)=x^2(1-5x) ?
The first derivative of f(x)=x^2(1-5x) is 2x-15x^2