What is the derivative of 500x-0.003x^2+10^{-8}x^3 ?

The derivative of 500x-0.003x^2+10^{-8}x^3 is 500-0.006x+0.00000003x^2

What is the first derivative of 500x-0.003x^2+10^{-8}x^3 ?

The first derivative of 500x-0.003x^2+10^{-8}x^3 is 500-0.006x+0.00000003x^2

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derivative of

500 x - 0.003 x^{2} + 1 0^{- 8} x^{3}

500 - 0.006 x + 0.00000003 x^{2}

Solution steps

\frac{d}{d x} (500 x - 0.003 x^{2} + 1 0^{- 8} x^{3})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (500 x) - \frac{d}{d x} (0.003 x^{2}) + \frac{d}{d x} (1 0^{- 8} x^{3})

\frac{d}{d x} (500 x) = 500

\frac{d}{d x} (0.003 x^{2}) = 0.006 x

\frac{d}{d x} (1 0^{- 8} x^{3}) = \frac{3 x ^{2}}{100000000}

= 500 - 0.006 x + \frac{3 x ^{2}}{100000000}

Simplify

= 500 - 0.006 x + 0.00000003 x^{2}

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What is the derivative of 500x-0.003x^2+10^{-8}x^3 ?
The derivative of 500x-0.003x^2+10^{-8}x^3 is 500-0.006x+0.00000003x^2
What is the first derivative of 500x-0.003x^2+10^{-8}x^3 ?
The first derivative of 500x-0.003x^2+10^{-8}x^3 is 500-0.006x+0.00000003x^2