Solve 5p+2t+3p-2t

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

Evaluate

$$8p$$

Solution Steps

Combine 5p and 3p to get 8p.

$$8p+2t-2t$$

Combine 2t and -2t to get 0.

$$8p$$

Differentiate w.r.t. p

$$8$$

Steps Using Definition of a Derivative

Combine 5p and 3p to get 8p.

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

Combine 2t and -2t to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}p}(8p)$$

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

$$8p^{1-1}$$

Subtract 1 from 1.

$$8p^{0}$$

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

$$8\times 1$$

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

$$8$$