Solve 8-5(0+p)+4p=

$$8 - 5 ( 0 + p ) + 4 p =$$

Evaluate

$$8-p$$

Solution Steps

Anything plus zero gives itself.

$$8-5p+4p$$

Combine -5p and 4p to get -p.

$$8-p$$

Differentiate w.r.t. p

$$-1$$

Steps Using Derivative Rule for Sum

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}p}(8-5p+4p)$$

Combine -5p and 4p to get -p.

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

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}.

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

Subtract 1 from 1.

$$-p^{0}$$

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

$$-1$$