Solve 9x*1left|2^2right|

$$9x \times 1 \left| { 2 }^{ 2 } \right|$$

Evaluate

$$36x$$

Solution Steps

Multiply 9 and 1 to get 9.

$$9x|2^{2}|$$

Calculate 2 to the power of 2 and get 4.

$$9x|4|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 4 is 4.

$$9x\times 4$$

Multiply 9 and 4 to get 36.

$$36x$$

Differentiate w.r.t. x

$$36$$

Steps Using Definition of a Derivative

Multiply 9 and 1 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x|2^{2}|)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x|4|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 4 is 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x\times 4)$$

Multiply 9 and 4 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x)$$

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

$$36x^{1-1}$$

Subtract 1 from 1.

$$36x^{0}$$

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

$$36\times 1$$

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

$$36$$