Solve x|-7|-5|-3|-2|0

$$x | - 7 | - 5 | - 3 | - 2 | 0$$

Evaluate

$$7x-15$$

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 -7 is 7.

$$x\times 7-5|-3|-2|0|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.

$$x\times 7-5\times 3-2|0|$$

Multiply 5 and 3 to get 15.

$$x\times 7-15-2|0|$$

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

$$x\times 7-15-2\times 0$$

Multiply 2 and 0 to get 0.

$$x\times 7-15-0$$

Multiply -1 and 0 to get 0.

$$x\times 7-15+0$$

Add -15 and 0 to get -15.

$$x\times 7-15$$

Differentiate w.r.t. x

$$7$$

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 -7 is 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 7-5|-3|-2|0|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -3 is 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 7-5\times 3-2|0|)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 7-15-2|0|)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 7-15-2\times 0)$$

Multiply 2 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 7-15-0)$$

Multiply -1 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 7-15+0)$$

Add -15 and 0 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 7-15)$$

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}.

$$7x^{1-1}$$

Subtract 1 from 1.

$$7x^{0}$$

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

$$7\times 1$$

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

$$7$$