Solve 4+8p-6p+5+20p

$$4 + 8 p - 6 p + 5 + 20 p$$

Evaluate

$$22p+9$$

Solution Steps

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

$$4+2p+5+20p$$

Add 4 and 5 to get 9.

$$9+2p+20p$$

Combine 2p and 20p to get 22p.

$$9+22p$$

Differentiate w.r.t. p

$$22$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(4+2p+5+20p)$$

Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}p}(9+2p+20p)$$

Combine 2p and 20p to get 22p.

$$\frac{\mathrm{d}}{\mathrm{d}p}(9+22p)$$

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}.

$$22p^{1-1}$$

Subtract 1 from 1.

$$22p^{0}$$

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

$$22\times 1$$

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

$$22$$