Solve 5t-3t+t+2t

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

Evaluate

$$5t$$

Solution Steps

Combine 5t and -3t to get 2t.

$$2t+t+2t$$

Combine 2t and t to get 3t.

$$3t+2t$$

Combine 3t and 2t to get 5t.

$$5t$$

Differentiate w.r.t. t

$$5$$

Steps Using Definition of a Derivative

Combine 5t and -3t to get 2t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(2t+t+2t)$$

Combine 2t and t to get 3t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(3t+2t)$$

Combine 3t and 2t to get 5t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(5t)$$

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

$$5t^{1-1}$$

Subtract 1 from 1.

$$5t^{0}$$

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

$$5\times 1$$

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

$$5$$