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Popular >

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

Solution

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

Solution

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

Solution steps

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

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{d c}{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{d c}{d x} = 0

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

Simplify

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

Popular Examples

derivative of 5x^2*ln(x)

\frac{d}{d x} (5 x^{2} \cdot ln (x))

(5x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=4

(5 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0, y (1) = 4

integral from 0 to 6 of (x^2-4)

\int_{0}^{6} (x^{2} - 4) d x

y^{^{'}} + 2 x y = x^{2}

derivative of f(x)=(4x^3-2x+1)/(x^2)derivative of

f (x) = \frac{4 x ^{3} - 2 x + 1}{x ^{2}}

Frequently Asked Questions (FAQ)

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