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Popular >

derivative of x^3+ax^2+bx+d

Solution

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

Solution

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

Solution steps

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

Treat

a, b, d

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{dd}{d x} = 0

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

Simplify

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

Popular Examples

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derivative of 3x^{-2x}derivative of

3 x^{- 2 x}

(\partial)/(\partial x)((mcT)/(mT))

\frac{\partial}{\partial x} (\frac{m c T}{m T})

Frequently Asked Questions (FAQ)

What is the derivative of x^3+ax^2+bx+d ?
The derivative of x^3+ax^2+bx+d is 3x^2+2ax+b
What is the first derivative of x^3+ax^2+bx+d ?
The first derivative of x^3+ax^2+bx+d is 3x^2+2ax+b