Solve f9/54

$$f \frac{ 9 }{ 5 } 4$$

Evaluate

$$\frac{36f}{5}$$

Solution Steps

Express \frac{9}{5}\times 4 as a single fraction.

$$f\times \frac{9\times 4}{5}$$

Multiply 9 and 4 to get 36.

$$f\times \frac{36}{5}$$

Differentiate w.r.t. f

$$\frac{36}{5} = 7\frac{1}{5} = 7.2$$

Steps Using Definition of a Derivative

Express \frac{9}{5}\times 4 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times \frac{9\times 4}{5})$$

Multiply 9 and 4 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times \frac{36}{5})$$

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

$$\frac{36}{5}f^{1-1}$$

Subtract 1 from 1.

$$\frac{36}{5}f^{0}$$

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

$$\frac{36}{5}\times 1$$

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

$$\frac{36}{5}$$