Solve 5t+2-7t+15-20

$$5 t + 2 - 7 t + 15 - 20$$

Evaluate

$$-2t-3$$

Solution Steps

Combine 5t and -7t to get -2t.

$$-2t+2+15-20$$

Add 2 and 15 to get 17.

$$-2t+17-20$$

Subtract 20 from 17 to get -3.

$$-2t-3$$

Differentiate w.r.t. t

$$-2$$

Steps Using Derivative Rule for Sum

Combine 5t and -7t to get -2t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(-2t+2+15-20)$$

Add 2 and 15 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}t}(-2t+17-20)$$

Subtract 20 from 17 to get -3.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-2t^{1-1}$$

Subtract 1 from 1.

$$-2t^{0}$$

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

$$-2$$