What is the derivative of x^2(1-4x) ?

The derivative of x^2(1-4x) is 2x-12x^2

What is the first derivative of x^2(1-4x) ?

The first derivative of x^2(1-4x) is 2x-12x^2

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derivative of

x^{2} (1 - 4 x)

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}

\frac{d}{d x} (x (x^{3} + 1)^{\frac{1}{3}})

\frac{d}{d x} (x a^{2} + x^{2})

t^{3} \cdot sin (3 t)

\frac{\partial}{\partial t} (cos (2 t))

\int \frac{1}{x 2 + x ^{2}} d x

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