Solve 5t+3t-2t

$$5 t + 3 t - 2 t$$

Evaluate

$$6t$$

Solution Steps

Combine 5t and 3t to get 8t.

$$8t-2t$$

Combine 8t and -2t to get 6t.

$$6t$$

Differentiate w.r.t. t

$$6$$

Steps Using Definition of a Derivative

Combine 5t and 3t to get 8t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(8t-2t)$$

Combine 8t and -2t to get 6t.

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

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

$$6t^{1-1}$$

Subtract 1 from 1.

$$6t^{0}$$

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

$$6\times 1$$

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

$$6$$