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Popular >

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

Solution

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

Solution

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

Popular Examples

derivative of f(x)=(2x^3)/3-12x derivative of

f (x) = \frac{2 x ^{3}}{3} - 12 x

derivative of (5x^3+4(3x^7-5))

\frac{d}{d x} ((5 x^{3} + 4) (3 x^{7} - 5))

area 2x^2-3x,(0,5)area

2 x^{2} - 3 x, (0, 5)

derivative of (3t-1)^4(2t+1)^{-3}derivative of

(3 t - 1)^{4} (2 t + 1)^{- 3}

integral of (x/(1+x^2))

\int (\frac{x}{1 + x ^{2}}) d x

Frequently Asked Questions (FAQ)

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