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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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