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Popular >

derivative of (x^3/3-(x^2)/2-6x+5)

Solution

\frac{d}{d x} (\frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x + 5)

Solution

x^{2} - x - 6

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{3} - \frac{x ^{2}}{2} - 6 x + 5)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{3}}{3}) - \frac{d}{d x} (\frac{x ^{2}}{2}) - \frac{d}{d x} (6 x) + \frac{d}{d x} (5)

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

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

\frac{d}{d x} (6 x) = 6

\frac{d}{d x} (5) = 0

= x^{2} - x - 6 + 0

Simplify

= x^{2} - x - 6

Popular Examples

f(x)=ln(sin(x^2+1))

f (x) = ln (sin (x^{2} + 1))

derivative of x^3-x^2-x+1

\frac{d}{d x} (x^{3} - x^{2} - x + 1)

integral of cos(x+pi/2)

\int cos (x + \frac{π}{2}) d x

tangent of y=-9/2 x^2+3x+3,(-1,-9/2)tangent of

y = - \frac{9}{2} x^{2} + 3 x + 3, (- 1, - \frac{9}{2})

limit as x approaches 2 of x^2-2

x \to 2 lim (x^{2} - 2)

Frequently Asked Questions (FAQ)

What is the derivative of (x^3/3-(x^2)/2-6x+5) ?
The derivative of (x^3/3-(x^2)/2-6x+5) is x^2-x-6
What is the first derivative of (x^3/3-(x^2)/2-6x+5) ?
The first derivative of (x^3/3-(x^2)/2-6x+5) is x^2-x-6