What is the derivative of 1-(1-0.01x^3) ?

The derivative of 1-(1-0.01x^3) is 0.000003x^2-0.0006x+0.03

What is the first derivative of 1-(1-0.01x^3) ?

The first derivative of 1-(1-0.01x^3) is 0.000003x^2-0.0006x+0.03

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\frac{d}{d x} (1 - (1 - 0.01 x)^{3})

0.000003 x^{2} - 0.0006 x + 0.03

Solution steps

\frac{d}{d x} (1 - (1 - 0.01 x)^{3})

Simplify

1 - (1 - 0.01 x)^{3} : 0.000001 x^{3} - 0.0003 x^{2} + 0.03 x

= \frac{d}{d x} (0.000001 x^{3} - 0.0003 x^{2} + 0.03 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (0.000001 x^{3}) - \frac{d}{d x} (0.0003 x^{2}) + \frac{d}{d x} (0.03 x)

\frac{d}{d x} (0.000001 x^{3}) = 0.000003 x^{2}

\frac{d}{d x} (0.0003 x^{2}) = 0.0006 x

\frac{d}{d x} (0.03 x) = 0.03

= 0.000003 x^{2} - 0.0006 x + 0.03

What is the derivative of 1-(1-0.01x^3) ?
The derivative of 1-(1-0.01x^3) is 0.000003x^2-0.0006x+0.03
What is the first derivative of 1-(1-0.01x^3) ?
The first derivative of 1-(1-0.01x^3) is 0.000003x^2-0.0006x+0.03