What is the derivative of ax^2+b ?

The derivative of ax^2+b is 2ax

What is the first derivative of ax^2+b ?

The first derivative of ax^2+b is 2ax

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

2 a x

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 2 a x + 0

Simplify

= 2 a x

\frac{d}{d x} (4 x ln (7 x) - 4 x)

\int - \frac{sec ^{2} ( x ) - 1}{tan ( x )} d x

\frac{s + 3}{s ^{2} + s + 1}

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{5}{x ^{4}}) (x + 9 x^{3}))

x \to 0 + lim (\frac{( 3 )}{x ^{2} - x})