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Popular >

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

Solution

derivative of

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

Popular Examples

integral of x^2e^{-2x^2}

\int x^{2} e^{- 2 x^{2}} d x

area y=1-x^2,y=3-3x area

y = 1 - x^{2}, y = 3 - 3 x

(\partial)/(\partial x)(2xy^4-2)

\frac{\partial}{\partial x} (2 x y^{4} - 2)

integral of (arcsin(x))

\int (arcsin (x)) d x

integral of (sin(2x))/(1+3sin^2(x))

\int \frac{sin ( 2 x )}{1 + 3 sin ^{2} ( x )} d x

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