What is the derivative of (x(x(a-bx))) ?

The derivative of (x(x(a-bx))) is 2ax-3bx^2

What is the first derivative of (x(x(a-bx))) ?

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

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\frac{d}{d x} ((x) (x (a - b x)))

2 a x - 3 b x^{2}

Solution steps

\frac{d}{d x} ((x) (x (a - b x)))

Simplify

(x) (x (a - b x)) : x^{2} (a - b x)

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

Apply the Product Rule:

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

f = x^{2}, g = a - b x

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

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

\frac{d}{d x} (a - b x) = - b

= 2 x (a - b x) + (- b) x^{2}

Simplify

2 x (a - b x) + (- b) x^{2} : 2 a x - 3 b x^{2}

= 2 a x - 3 b x^{2}

π (1 - x^{2})^{2}

(8 z) (x y)

\frac{d}{d t} ((x) (x - 2 y))

\frac{k}{( a - x ) ( b - x )}

\frac{e ^{- s}}{s ^{2} ( s + 1 )}

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