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

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

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

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

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derivative of

1 - (1 - 0.01 t)^{3}

0.000003 t^{2} - 0.0006 t + 0.03

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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