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

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

- 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

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