Solve varepsilon/125^3

$$\frac { \varepsilon } { 125 ^ { 3 } }$$

Differentiate w.r.t. ε

$$\frac{1}{1953125} = 5.12 \times 10^{-7}$$

Steps Using Definition of a Derivative

Calculate 125 to the power of 3 and get 1953125.

$$\frac{\mathrm{d}}{\mathrm{d}\epsilon }(\frac{\epsilon }{1953125})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{1953125}\epsilon ^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{1953125}\epsilon ^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{1953125}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{1953125}$$

Evaluate

$$\frac{\epsilon }{1953125}$$

Solution Steps

Calculate 125 to the power of 3 and get 1953125.

$$\frac{\epsilon }{1953125}$$