Solve 2*2/2^5quadb)^2^3+

$$\frac { 2 \cdot 2 } { 2 ^ { 5 } } \quad b ) ^ { 2 ^ { 3 } + }$$

Evaluate

$$\frac{b}{8}$$

Solution Steps

Cancel out 2\times 2 in both numerator and denominator.

$$\frac{1}{2^{3}}b$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1}{8}b$$

Differentiate w.r.t. b

$$\frac{1}{8} = 0.125$$

Steps Using Definition of a Derivative

Cancel out 2\times 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{2^{3}}b)$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{8}b)$$

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

$$\frac{1}{8}b^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{8}b^{0}$$

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

$$\frac{1}{8}\times 1$$

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

$$\frac{1}{8}$$