Solve -3t-(-4t)+7t+2t-5t+(-3t)-(-t)

$$- 3 t - ( - 4 t ) + 7 t + 2 t - 5 t + ( - 3 t ) - ( - t )$$

Evaluate

$$3t$$

Solution Steps

The opposite of -4t is 4t.

$$-3t+4t+7t+2t-5t-3t-\left(-t\right)$$

Combine -3t and 4t to get t.

$$t+7t+2t-5t-3t-\left(-t\right)$$

Combine t and 7t to get 8t.

$$8t+2t-5t-3t-\left(-t\right)$$

Combine 8t and 2t to get 10t.

$$10t-5t-3t-\left(-t\right)$$

Combine 10t and -5t to get 5t.

$$5t-3t-\left(-t\right)$$

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

$$2t-\left(-t\right)$$

Multiply -1 and -1 to get 1.

$$2t+t$$

Combine 2t and t to get 3t.

$$3t$$

Differentiate w.r.t. t

$$3$$

Steps Using Definition of a Derivative

The opposite of -4t is 4t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(-3t+4t+7t+2t-5t-3t-\left(-t\right))$$

Combine -3t and 4t to get t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(t+7t+2t-5t-3t-\left(-t\right))$$

Combine t and 7t to get 8t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(8t+2t-5t-3t-\left(-t\right))$$

Combine 8t and 2t to get 10t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(10t-5t-3t-\left(-t\right))$$

Combine 10t and -5t to get 5t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(5t-3t-\left(-t\right))$$

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

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

Multiply -1 and -1 to get 1.

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

Combine 2t and t to get 3t.

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

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

$$3t^{1-1}$$

Subtract 1 from 1.

$$3t^{0}$$

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

$$3\times 1$$

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

$$3$$