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Popular Calculus >

derivative of 900x-1/3 x^3+2500

Solution

\frac{d}{d x} (900 x - \frac{1}{3} x^{3} + 2500)

Solution

- x^{2} + 900

Solution steps

\frac{d}{d x} (900 x - \frac{1}{3} x^{3} + 2500)

Simplify

900 x - \frac{1}{3} x^{3} + 2500 : 900 x - \frac{x ^{3}}{3} + 2500

= \frac{d}{d x} (900 x - \frac{x ^{3}}{3} + 2500)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (900 x) - \frac{d}{d x} (\frac{x ^{3}}{3}) + \frac{d}{d x} (2500)

\frac{d}{d x} (900 x) = 900

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

\frac{d}{d x} (2500) = 0

= 900 - x^{2} + 0

Simplify

= - x^{2} + 900

Graph

Popular Examples

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

\int \frac{- x + 1}{x ^{2} + x + 1} d x

5y^{''}+5y^'-10y=0

5 y^{^{''}} + 5 y^{^{'}} - 10 y = 0

integral from-infinity to 0 of (4-3x)e^x

\int_{- \infty}^{0} (4 - 3 x) e^{x} d x

integral from 0 to 4 of 3/(x^2)

\int_{0}^{4} \frac{3}{x ^{2}} d x

(d^2)/(dx^2)(5e^x)

\frac{d ^{2}}{d x ^{2}} (5 e^{x})

Frequently Asked Questions (FAQ)

What is the derivative of 900x-1/3 x^3+2500 ?
The derivative of 900x-1/3 x^3+2500 is -x^2+900
What is the first derivative of 900x-1/3 x^3+2500 ?
The first derivative of 900x-1/3 x^3+2500 is -x^2+900