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

The derivative of f(x)=x(x+3)^2 is 3x^2+12x+9

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

The first derivative of f(x)=x(x+3)^2 is 3x^2+12x+9

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derivative of

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

3 x^{2} + 12 x + 9

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

1 \cdot (x + 3)^{2} + 2 (x + 3) x : 3 x^{2} + 12 x + 9

= 3 x^{2} + 12 x + 9

\int_{4}^{\infty} \frac{1}{x ^{3}} d x

y^{^{'}} - 2 y = 7

\frac{\partial}{\partial x} (x + yz)

\frac{d}{d x} (6 + x)

x \to 0 lim (\frac{\frac{8}{1 + x} - 8}{x})

What is the derivative of f(x)=x(x+3)^2 ?
The derivative of f(x)=x(x+3)^2 is 3x^2+12x+9
What is the first derivative of f(x)=x(x+3)^2 ?
The first derivative of f(x)=x(x+3)^2 is 3x^2+12x+9