Solve f(12)^3div(2)^4=

$$f ( 12 ) ^ { 3 } \div ( 2 ) ^ { 4 } =$$

Evaluate

$$108f$$

Solution Steps

Calculate 12 to the power of 3 and get 1728.

$$\frac{f\times 1728}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{f\times 1728}{16}$$

Divide f\times 1728 by 16 to get f\times 108.

$$f\times 108$$

Differentiate w.r.t. f

$$108$$

Steps Using Definition of a Derivative

Calculate 12 to the power of 3 and get 1728.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f\times 1728}{2^{4}})$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f\times 1728}{16})$$

Divide f\times 1728 by 16 to get f\times 108.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times 108)$$

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

$$108f^{1-1}$$

Subtract 1 from 1.

$$108f^{0}$$

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

$$108\times 1$$

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

$$108$$