Solve t+5t-2t

$$t + 5 t - 2 t$$

Evaluate

$$4t$$

Solution Steps

Combine t and 5t to get 6t.

$$6t-2t$$

Combine 6t and -2t to get 4t.

$$4t$$

Differentiate w.r.t. t

$$4$$

Steps Using Definition of a Derivative

Combine t and 5t to get 6t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(6t-2t)$$

Combine 6t and -2t to get 4t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(4t)$$

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

$$4t^{1-1}$$

Subtract 1 from 1.

$$4t^{0}$$

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

$$4\times 1$$

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

$$4$$