Solve b|(-2)^-6

$$b | ( - 2 ) ^ { - 6 }$$

Evaluate

$$\frac{b}{64}$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$b\times 2^{-6}$$

Calculate 2 to the power of -6 and get \frac{1}{64}.

$$b\times \frac{1}{64}$$

Differentiate w.r.t. b

$$\frac{1}{64} = 0.015625$$

Steps Using Definition of a Derivative

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b\times 2^{-6})$$

Calculate 2 to the power of -6 and get \frac{1}{64}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b\times \frac{1}{64})$$

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

$$\frac{1}{64}b^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{64}b^{0}$$

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

$$\frac{1}{64}\times 1$$

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

$$\frac{1}{64}$$