What is the derivative of x(24-2x(24-2x)) ?

The derivative of x(24-2x(24-2x)) is 12x^2-192x+576

What is the first derivative of x(24-2x(24-2x)) ?

The first derivative of x(24-2x(24-2x)) is 12x^2-192x+576

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\frac{d}{d x} (x (24 - 2 x) (24 - 2 x))

12 x^{2} - 192 x + 576

Solution steps

\frac{d}{d x} (x (24 - 2 x) (24 - 2 x))

Simplify

x (24 - 2 x) (24 - 2 x) : x (24 - 2 x)^{2}

= \frac{d}{d x} (x (24 - 2 x)^{2})

Apply the Product Rule:

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

f = x, g = (24 - 2 x)^{2}

= \frac{d x}{d x} (24 - 2 x)^{2} + \frac{d}{d x} ((24 - 2 x)^{2}) x

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

\frac{d}{d x} ((24 - 2 x)^{2}) = - 4 (24 - 2 x)

= 1 \cdot (24 - 2 x)^{2} + (- 4 (24 - 2 x)) x

Simplify

1 \cdot (24 - 2 x)^{2} + (- 4 (24 - 2 x)) x : 12 x^{2} - 192 x + 576

= 12 x^{2} - 192 x + 576

x \to - 2 lim (\frac{5 x + 2}{x - 2})

\int \frac{1}{0.02 y - 6} d y

f (x) = x^{- 1}

\int_{0}^{2 π} \frac{1 - cos ( x )}{2} d x

\int \frac{x ^{2} - 16}{x ^{4}} d x

What is the derivative of x(24-2x(24-2x)) ?
The derivative of x(24-2x(24-2x)) is 12x^2-192x+576
What is the first derivative of x(24-2x(24-2x)) ?
The first derivative of x(24-2x(24-2x)) is 12x^2-192x+576