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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int 5 (5 x - 1)^{3} d x

\int e^{x} + x cos (y) d y

n = 1 \sum \infty n^{3} \cdot e^{- n^{2}}

x \to 4 lim (5 x^{2} - 2 x)

\frac{4 + t}{t e ^{t}}

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