Solve 4-15-3p-4p+20

$$4-15-3p-4p+20$$

Evaluate

$$9-7p$$

Solution Steps

Subtract 15 from 4 to get -11.

$$-11-3p-4p+20$$

Combine -3p and -4p to get -7p.

$$-11-7p+20$$

Add -11 and 20 to get 9.

$$9-7p$$

Differentiate w.r.t. p

$$-7$$

Steps Using Derivative Rule for Sum

Subtract 15 from 4 to get -11.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-11-3p-4p+20)$$

Combine -3p and -4p to get -7p.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-11-7p+20)$$

Add -11 and 20 to get 9.

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

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}.

$$-7p^{1-1}$$

Subtract 1 from 1.

$$-7p^{0}$$

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

$$-7$$