What is the derivative of f(x)=x(8-x)^3 ?

The derivative of f(x)=x(8-x)^3 is (8-x)^3-3x(8-x)^2

What is the first derivative of f(x)=x(8-x)^3 ?

The first derivative of f(x)=x(8-x)^3 is (8-x)^3-3x(8-x)^2

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derivative of

f (x) = x (8 - x)^{3}

(8 - x)^{3} - 3 x (8 - x)^{2}

Solution steps

\frac{d}{d x} (x (8 - x)^{3})

Apply the Product Rule:

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

f = x, g = (8 - x)^{3}

= \frac{d x}{d x} (8 - x)^{3} + \frac{d}{d x} ((8 - x)^{3}) x

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

\frac{d}{d x} ((8 - x)^{3}) = - 3 (8 - x)^{2}

= 1 \cdot (8 - x)^{3} + (- 3 (8 - x)^{2}) x

Simplify

= (8 - x)^{3} - 3 x (8 - x)^{2}

What is the derivative of f(x)=x(8-x)^3 ?
The derivative of f(x)=x(8-x)^3 is (8-x)^3-3x(8-x)^2
What is the first derivative of f(x)=x(8-x)^3 ?
The first derivative of f(x)=x(8-x)^3 is (8-x)^3-3x(8-x)^2