Solve h/(2^1+8-1+1

$$\frac { h } { ( 2 ^ { 1 + 8 - 1 } + 1 }$$

Evaluate

$$\frac{h}{257}$$

Solution Steps

Add 1 and 8 to get 9.

$$\frac{h}{2^{9-1}+1}$$

Subtract 1 from 9 to get 8.

$$\frac{h}{2^{8}+1}$$

Calculate 2 to the power of 8 and get 256.

$$\frac{h}{256+1}$$

Add 256 and 1 to get 257.

$$\frac{h}{257}$$

Differentiate w.r.t. h

$$\frac{1}{257} = 0.0038910505836575876$$

Steps Using Definition of a Derivative

Add 1 and 8 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{h}{2^{9-1}+1})$$

Subtract 1 from 9 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{h}{2^{8}+1})$$

Calculate 2 to the power of 8 and get 256.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{h}{256+1})$$

Add 256 and 1 to get 257.

$$\frac{\mathrm{d}}{\mathrm{d}h}(\frac{h}{257})$$

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

$$\frac{1}{257}h^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{257}h^{0}$$

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

$$\frac{1}{257}\times 1$$

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

$$\frac{1}{257}$$