Solve c|(-1)^3

$$c | ( - 1 ) ^ { 3 }$$

Evaluate

$$c$$

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 -1 is 1.

$$c\times 1^{3}$$

Calculate 1 to the power of 3 and get 1.

$$c\times 1$$

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

$$c$$

Differentiate w.r.t. c

$$1$$

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 -1 is 1.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c\times 1^{3})$$

Calculate 1 to the power of 3 and get 1.

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

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

$$c^{1-1}$$

Subtract 1 from 1.

$$c^{0}$$

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

$$1$$