What is the derivative of ax^3+bx^2+c ?

The derivative of ax^3+bx^2+c is 3ax^2+2bx

What is the first derivative of ax^3+bx^2+c ?

The first derivative of ax^3+bx^2+c is 3ax^2+2bx

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\frac{d}{d x} (a x^{3} + b x^{2} + c)

3 a x^{2} + 2 b x

Solution steps

\frac{d}{d x} (a x^{3} + b x^{2} + c)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (a x^{3}) + \frac{d}{d x} (b x^{2}) + \frac{d c}{d x}

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

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

\frac{d c}{d x} = 0

= 3 a x^{2} + 2 b x + 0

Simplify

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

What is the derivative of ax^3+bx^2+c ?
The derivative of ax^3+bx^2+c is 3ax^2+2bx
What is the first derivative of ax^3+bx^2+c ?
The first derivative of ax^3+bx^2+c is 3ax^2+2bx