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Popular >

derivative of x^3(1-x^2)

Solution

\frac{d}{d x} (x^{3} (1 - x)^{2})

Solution

5 x^{4} - 8 x^{3} + 3 x^{2}

Solution steps

\frac{d}{d x} (x^{3} (1 - x)^{2})

Apply the Product Rule:

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

f = x^{3}, g = (1 - x)^{2}

= \frac{d}{d x} (x^{3}) (1 - x)^{2} + \frac{d}{d x} ((1 - x)^{2}) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} (1 - x)^{2} + (- 2 (1 - x)) x^{3}

Simplify

3 x^{2} (1 - x)^{2} + (- 2 (1 - x)) x^{3} : 5 x^{4} - 8 x^{3} + 3 x^{2}

= 5 x^{4} - 8 x^{3} + 3 x^{2}

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Frequently Asked Questions (FAQ)

What is the derivative of x^3(1-x^2) ?
The derivative of x^3(1-x^2) is 5x^4-8x^3+3x^2
What is the first derivative of x^3(1-x^2) ?
The first derivative of x^3(1-x^2) is 5x^4-8x^3+3x^2