What is the derivative of f(x)=ax^2+bx+c ?

The derivative of f(x)=ax^2+bx+c is 2ax+b

What is the first derivative of f(x)=ax^2+bx+c ?

The first derivative of f(x)=ax^2+bx+c is 2ax+b

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derivative

2 a x + b

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= 2 a x + b + 0

Simplify

= 2 a x + b

What is the derivative of f(x)=ax^2+bx+c ?
The derivative of f(x)=ax^2+bx+c is 2ax+b
What is the first derivative of f(x)=ax^2+bx+c ?
The first derivative of f(x)=ax^2+bx+c is 2ax+b