Solve v/2^8-v/2^9

$$\frac { v } { 2 ^ { 8 } } - \frac { v } { 2 ^ { 9 } }$$

Evaluate

$$\frac{v}{512}$$

Solution Steps

Calculate 2 to the power of 8 and get 256.

$$\frac{v}{256}-\frac{v}{2^{9}}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{v}{256}-\frac{v}{512}$$

Combine \frac{v}{256} and -\frac{v}{512} to get \frac{1}{512}v.

$$\frac{1}{512}v$$

Differentiate w.r.t. v

$$\frac{1}{512} = 0.001953125$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 8 and get 256.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v}{256}-\frac{v}{2^{9}})$$

Calculate 2 to the power of 9 and get 512.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v}{256}-\frac{v}{512})$$

Combine \frac{v}{256} and -\frac{v}{512} to get \frac{1}{512}v.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{512}v)$$

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

$$\frac{1}{512}v^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{512}v^{0}$$

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

$$\frac{1}{512}\times 1$$

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

$$\frac{1}{512}$$