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Popular >

derivative of x^2(1-x^2)

Solution

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

Solution

4 x^{3} - 6 x^{2} + 2 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (1 - x)^{2} + (- 2 (1 - x)) x^{2} : 4 x^{3} - 6 x^{2} + 2 x

= 4 x^{3} - 6 x^{2} + 2 x

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\int_{- 1}^{2} x e^{6 x} d x

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Frequently Asked Questions (FAQ)

What is the derivative of x^2(1-x^2) ?
The derivative of x^2(1-x^2) is 4x^3-6x^2+2x
What is the first derivative of x^2(1-x^2) ?
The first derivative of x^2(1-x^2) is 4x^3-6x^2+2x