What is the derivative of Ax^2+Bx+C ?

The derivative of Ax^2+Bx+C is 2Ax+B

What is the first derivative of Ax^2+Bx+C ?

The first derivative of Ax^2+Bx+C is 2Ax+B

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\frac{d}{d x} (A x^{2} + B x + C)

2 A x + B

Solution steps

\frac{d}{d x} (A x^{2} + B x + C)

Treat

A, B, C

as constants

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

\int \frac{x ^{2}}{( x ^{2} + 4 ) ( x + 2 )} d x

b + x^{2} - k ln (\frac{( x + 1 ) ( x - 1 )}{k}) - 1

\frac{2 x}{1 + x ^{2}}

\int \frac{x + 9}{2 x ^{3} - 18 x} d x

2 \frac{d y}{d x} + 18 y = 9

What is the derivative of Ax^2+Bx+C ?
The derivative of Ax^2+Bx+C is 2Ax+B
What is the first derivative of Ax^2+Bx+C ?
The first derivative of Ax^2+Bx+C is 2Ax+B