Solve f(2^-0)^3=

$$f ( 2 ^ { - 0 } ) ^ { 3 } =$$

Evaluate

$$f$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 0 and 3 to get 0.

$$f\times 2^{0}$$

Calculate 2 to the power of 0 and get 1.

$$f\times 1$$

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

$$f$$

Differentiate w.r.t. f

$$1$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 0 and 3 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times 2^{0})$$

Calculate 2 to the power of 0 and get 1.

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

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

$$f^{1-1}$$

Subtract 1 from 1.

$$f^{0}$$

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

$$1$$