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

The derivative of x^3(3x+1) is 12x^3+3x^2

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

The first derivative of x^3(3x+1) is 12x^3+3x^2

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = 3 x + 1

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{1}{x ^{2} - x - 6})

x \frac{d y}{d x} = y + x e^{\frac{y}{x}}

\int_{0}^{\frac{π}{3}} sin^{3} (x) d x

\int (1 - r) r d r

\frac{\partial}{\partial y} (- 2 x)

What is the derivative of x^3(3x+1) ?
The derivative of x^3(3x+1) is 12x^3+3x^2
What is the first derivative of x^3(3x+1) ?
The first derivative of x^3(3x+1) is 12x^3+3x^2