Solve 5f+6f+f/4

$$5 f + 6 f + \frac { f } { 4 }$$

Evaluate

$$\frac{45f}{4}$$

Solution Steps

Combine 5f and 6f to get 11f.

$$11f+\frac{f}{4}$$

Combine 11f and \frac{f}{4} to get \frac{45}{4}f.

$$\frac{45}{4}f$$

Differentiate w.r.t. f

$$\frac{45}{4} = 11\frac{1}{4} = 11.25$$

Steps Using Definition of a Derivative

Combine 5f and 6f to get 11f.

$$\frac{\mathrm{d}}{\mathrm{d}f}(11f+\frac{f}{4})$$

Combine 11f and \frac{f}{4} to get \frac{45}{4}f.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{45}{4}f)$$

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

$$\frac{45}{4}f^{1-1}$$

Subtract 1 from 1.

$$\frac{45}{4}f^{0}$$

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

$$\frac{45}{4}\times 1$$

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

$$\frac{45}{4}$$