Solve A|2|3|8|3|7

$$A | 2 | 3 | 8 | 3 | 7$$

Evaluate

$$1008A$$

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 2 is 2.

$$A\times 2\times 3|8|\times 3|7|$$

Multiply 2 and 3 to get 6.

$$A\times 6|8|\times 3|7|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 8 is 8.

$$A\times 6\times 8\times 3|7|$$

Multiply 6 and 8 to get 48.

$$A\times 48\times 3|7|$$

Multiply 48 and 3 to get 144.

$$A\times 144|7|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 7 is 7.

$$A\times 144\times 7$$

Multiply 144 and 7 to get 1008.

$$A\times 1008$$

Differentiate w.r.t. A

$$1008$$

Steps Using Definition of a Derivative

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 2 is 2.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 2\times 3|8|\times 3|7|)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 6|8|\times 3|7|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 8 is 8.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 6\times 8\times 3|7|)$$

Multiply 6 and 8 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 48\times 3|7|)$$

Multiply 48 and 3 to get 144.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 144|7|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 7 is 7.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 144\times 7)$$

Multiply 144 and 7 to get 1008.

$$\frac{\mathrm{d}}{\mathrm{d}A}(A\times 1008)$$

The derivative of ax^{n} is nax^{n-1}.

$$1008A^{1-1}$$

Subtract 1 from 1.

$$1008A^{0}$$

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

$$1008\times 1$$

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

$$1008$$