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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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