What is the derivative of (ax-b(cx^2)) ?

The derivative of (ax-b(cx^2)) is c(3ax^2-2bx)

What is the first derivative of (ax-b(cx^2)) ?

The first derivative of (ax-b(cx^2)) is c(3ax^2-2bx)

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

c (3 a x^{2} - 2 b x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Expand

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

= c (3 a x^{2} - 2 b x)

What is the derivative of (ax-b(cx^2)) ?
The derivative of (ax-b(cx^2)) is c(3ax^2-2bx)
What is the first derivative of (ax-b(cx^2)) ?
The first derivative of (ax-b(cx^2)) is c(3ax^2-2bx)