Solve 2^-2*5^-3v

$$2 ^ { - 2 } \times 5 ^ { - 3 } v$$

Evaluate

$$\frac{v}{500}$$

Solution Steps

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{1}{4}\times 5^{-3}v$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{1}{4}\times \frac{1}{125}v$$

Multiply \frac{1}{4} and \frac{1}{125} to get \frac{1}{500}.

$$\frac{1}{500}v$$

Differentiate w.r.t. v

$$\frac{1}{500} = 0.002$$

Steps Using Definition of a Derivative

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{4}\times 5^{-3}v)$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{4}\times \frac{1}{125}v)$$

Multiply \frac{1}{4} and \frac{1}{125} to get \frac{1}{500}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{500}v)$$

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

$$\frac{1}{500}v^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{500}v^{0}$$

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

$$\frac{1}{500}\times 1$$

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

$$\frac{1}{500}$$