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

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

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

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

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

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

Solution steps

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

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}{d x} (c x) + \frac{dd}{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}{d x} (c x) = c

\frac{dd}{d x} = 0

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

Simplify

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

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