Solve 3f+f+0.5f

$$3 f + f + 0.5 f$$

Evaluate

$$\frac{9f}{2}$$

Solution Steps

Combine 3f and f to get 4f.

$$4f+0.5f$$

Combine 4f and 0.5f to get 4.5f.

$$4.5f$$

Differentiate w.r.t. f

$$4.5$$

Steps Using Definition of a Derivative

Combine 3f and f to get 4f.

$$\frac{\mathrm{d}}{\mathrm{d}f}(4f+0.5f)$$

Combine 4f and 0.5f to get 4.5f.

$$\frac{\mathrm{d}}{\mathrm{d}f}(4.5f)$$

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

$$4.5f^{1-1}$$

Subtract 1 from 1.

$$4.5f^{0}$$

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

$$4.5\times 1$$

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

$$4.5$$