Solve |11|[5.01Q+3.442)

$$| 11 | [ 5.01 Q + 3.442 )$$

Evaluate

$$\frac{5511Q}{100}+37.862$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 11 is 11.

$$11\left(5.01Q+3.442\right)$$

Use the distributive property to multiply 11 by 5.01Q+3.442.

$$55.11Q+37.862$$

Differentiate w.r.t. Q

$$55.11$$

Steps Using Derivative Rule for Sum

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 11 is 11.

$$\frac{\mathrm{d}}{\mathrm{d}Q}(11\left(5.01Q+3.442\right))$$

Use the distributive property to multiply 11 by 5.01Q+3.442.

$$\frac{\mathrm{d}}{\mathrm{d}Q}(55.11Q+37.862)$$

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}.

$$55.11Q^{1-1}$$

Subtract 1 from 1.

$$55.11Q^{0}$$

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

$$55.11\times 1$$

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

$$55.11$$