What is (\partial)/(\partial x)(n^2x*(1-x)^n) ?

The answer to (\partial)/(\partial x)(n^2x*(1-x)^n) is n^2((1-x)^n-nx(1-x)^{n-1})

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(\partial)/(\partial x)(n^2x*(1-x)^n)

\frac{\partial}{\partial x} (n^{2} x \cdot (1 - x)^{n})

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

Solution steps

\frac{\partial}{\partial x} (n^{2} x (1 - x)^{n})

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} ((1 - x)^{n}) = - n (1 - x)^{n - 1}

= n^{2} (1 \cdot (1 - x)^{n} + (- n (1 - x)^{n - 1}) x)

Simplify

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

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What is (\partial)/(\partial x)(n^2x*(1-x)^n) ?
The answer to (\partial)/(\partial x)(n^2x*(1-x)^n) is n^2((1-x)^n-nx(1-x)^{n-1})