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

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

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

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

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derivative of

x (3 - x)^{3}

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

f (x) = x^{2} cos (\frac{1}{x})

y = \frac{x + 1}{x - 1}

n = 2 \sum \infty \frac{1}{n ln ( n )}

x \to 0 lim (\frac{4 cos ( x ) - 4}{x})

\frac{\partial}{\partial x} (6 x yz)

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