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

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

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

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

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derivative of

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

3 x^{2} + 2 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 3 x^{2} + 2 x

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