What is the derivative of f(x)=x(1-x)^4 ?

The derivative of f(x)=x(1-x)^4 is (1-x)^4-4x(1-x)^3

What is the first derivative of f(x)=x(1-x)^4 ?

The first derivative of f(x)=x(1-x)^4 is (1-x)^4-4x(1-x)^3

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derivative of

f (x) = x (1 - x)^{4}

(1 - x)^{4} - 4 x (1 - x)^{3}

Solution steps

\frac{d}{d x} (x (1 - x)^{4})

Apply the Product Rule:

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

f = x, g = (1 - x)^{4}

= \frac{d x}{d x} (1 - x)^{4} + \frac{d}{d x} ((1 - x)^{4}) x

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

\frac{d}{d x} ((1 - x)^{4}) = - 4 (1 - x)^{3}

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

Simplify

= (1 - x)^{4} - 4 x (1 - x)^{3}

What is the derivative of f(x)=x(1-x)^4 ?
The derivative of f(x)=x(1-x)^4 is (1-x)^4-4x(1-x)^3
What is the first derivative of f(x)=x(1-x)^4 ?
The first derivative of f(x)=x(1-x)^4 is (1-x)^4-4x(1-x)^3