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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int 3^{3 x} d x

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