What is (\partial)/(\partial x)(x(x+1)^2) ?

The answer to (\partial)/(\partial x)(x(x+1)^2) is 3x^2+4x+1

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(\partial)/(\partial x)(x(x+1)^2)

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

3 x^{2} + 4 x + 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (x + 1)^{2} + 2 (x + 1) x : 3 x^{2} + 4 x + 1

= 3 x^{2} + 4 x + 1

n = 1 \sum \infty \frac{4}{n ^{2} + 5 n + 6}

\int \frac{sin ( \frac{9}{x} )}{x ^{2}} d x

\frac{\partial}{\partial x} (x^{2} - 10 x + y^{2} + 8)

\frac{1}{( s ^{3} + 4 s )}

10 (t - 1)

What is (\partial)/(\partial x)(x(x+1)^2) ?
The answer to (\partial)/(\partial x)(x(x+1)^2) is 3x^2+4x+1