Solve c_{4}(1/2)^4(1/8)^0

$$c _ { 4 } ( \frac { 1 } { 2 } ) ^ { 4 } ( \frac { 1 } { 8 } ) ^ { 0 }$$

Evaluate

$$\frac{c_{4}}{16}$$

Solution Steps

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$c_{4}\times \frac{1}{16}\times \left(\frac{1}{8}\right)^{0}$$

Calculate \frac{1}{8} to the power of 0 and get 1.

$$c_{4}\times \frac{1}{16}\times 1$$

Multiply \frac{1}{16} and 1 to get \frac{1}{16}.

$$c_{4}\times \frac{1}{16}$$

Differentiate w.r.t. c_4

$$\frac{1}{16} = 0.0625$$

Steps Using Definition of a Derivative

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}c_{4}}(c_{4}\times \frac{1}{16}\times \left(\frac{1}{8}\right)^{0})$$

Calculate \frac{1}{8} to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}c_{4}}(c_{4}\times \frac{1}{16}\times 1)$$

Multiply \frac{1}{16} and 1 to get \frac{1}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}c_{4}}(c_{4}\times \frac{1}{16})$$

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

$$\frac{1}{16}c_{4}^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{16}c_{4}^{0}$$

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

$$\frac{1}{16}\times 1$$

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

$$\frac{1}{16}$$