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Popular >

derivative of x^{(3)}+ax^{(2)}+bx+c

Solution

derivative of

x^{(3)} + a \cdot x^{(2)} + b \cdot 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 sqrt(2x-9)

\frac{d}{d x} (2 x - 9)

integral of (x-1)^{1/2}

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

simplify x/5+(sqrt(x^2-100x+6100))/(1.1)simplify

\frac{x}{5} + \frac{x ^{2} - 100 x + 6100}{1.1}

integral of sin(y)cosh(x)

\int sin (y) cosh (x) d y

limit as x approaches 0 of 1

x \to 0 lim (1)

Frequently Asked Questions (FAQ)

What is the derivative of x^{(3)}+a*x^{(2)}+b*x+c ?
The derivative of x^{(3)}+a*x^{(2)}+b*x+c is 3x^2+2ax+b
What is the first derivative of x^{(3)}+a*x^{(2)}+b*x+c ?
The first derivative of x^{(3)}+a*x^{(2)}+b*x+c is 3x^2+2ax+b