What is the derivative of 3x^2(1-x)^3 ?

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

What is the first derivative of 3x^2(1-x)^3 ?

The first derivative of 3x^2(1-x)^3 is 3(2x(1-x)^3-3x^2(1-x)^2)

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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