What is the derivative of x(4-x^3) ?

The derivative of x(4-x^3) is (4-x)^3-3x(4-x)^2

What is the first derivative of x(4-x^3) ?

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

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\frac{d}{d x} (x (4 - x)^{3})

(4 - x)^{3} - 3 x (4 - x)^{2}

Solution steps

\frac{d}{d x} (x (4 - x)^{3})

Apply the Product Rule:

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

f = x, g = (4 - x)^{3}

= \frac{d x}{d x} (4 - x)^{3} + \frac{d}{d x} ((4 - x)^{3}) x

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

\frac{d}{d x} ((4 - x)^{3}) = - 3 (4 - x)^{2}

= 1 \cdot (4 - x)^{3} + (- 3 (4 - x)^{2}) x

Simplify

= (4 - x)^{3} - 3 x (4 - x)^{2}

\int \frac{1}{2 + t} d t

\frac{d}{d x} (7 x^{5} - 3 x^{2} - x + 5)

x \to 2 lim (\frac{x ^{3}}{x - 2})

\int_{0}^{\frac{π}{4}} (tan^{2} (x)) d x

\frac{d}{d x} (5 x^{2} - 2 x + 1)

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