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

The derivative of x^2(x+1^2) is 4x^3+6x^2+2x

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

The first derivative of x^2(x+1^2) is 4x^3+6x^2+2x

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

4 x^{3} + 6 x^{2} + 2 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x + 1)^{2} + 2 (x + 1) x^{2} : 4 x^{3} + 6 x^{2} + 2 x

= 4 x^{3} + 6 x^{2} + 2 x

What is the derivative of x^2(x+1^2) ?
The derivative of x^2(x+1^2) is 4x^3+6x^2+2x
What is the first derivative of x^2(x+1^2) ?
The first derivative of x^2(x+1^2) is 4x^3+6x^2+2x