Solve 5^-1quadtext{(c)}1

$$5 ^ { - 1 } \quad \text { (c) } 1$$

Evaluate

$$\frac{c}{5}$$

Solution Steps

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\frac{1}{5}c\times 1$$

Multiply \frac{1}{5} and 1 to get \frac{1}{5}.

$$\frac{1}{5}c$$

Differentiate w.r.t. c

$$\frac{1}{5} = 0.2$$

Steps Using Definition of a Derivative

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{1}{5}c\times 1)$$

Multiply \frac{1}{5} and 1 to get \frac{1}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{1}{5}c)$$

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

$$\frac{1}{5}c^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{5}c^{0}$$

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

$$\frac{1}{5}\times 1$$

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

$$\frac{1}{5}$$