Solve p+7-4p+4p+8p

$$p + 7 - 4 p + 4 p + 8 p$$

Evaluate

$$9p+7$$

Solution Steps

Combine p and -4p to get -3p.

$$-3p+7+4p+8p$$

Combine -3p and 4p to get p.

$$p+7+8p$$

Combine p and 8p to get 9p.

$$9p+7$$

Differentiate w.r.t. p

$$9$$

Steps Using Derivative Rule for Sum

Combine p and -4p to get -3p.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-3p+7+4p+8p)$$

Combine -3p and 4p to get p.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p+7+8p)$$

Combine p and 8p to get 9p.

$$\frac{\mathrm{d}}{\mathrm{d}p}(9p+7)$$

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}.

$$9p^{1-1}$$

Subtract 1 from 1.

$$9p^{0}$$

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

$$9\times 1$$

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

$$9$$