Solve 2x^0(2x)^0/2x

$$\frac { 2 x ^ { 0 } ( 2 x ) ^ { 0 } } { 2 x }$$

Evaluate

$$\frac{1}{x}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{x^{0}\times \left(2x\right)^{0}}{x}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\left(2x\right)^{0}}{x^{1}}$$

Calculate 2x to the power of 0 and get 1.

$$\frac{1}{x^{1}}$$

Calculate x to the power of 1 and get x.

$$\frac{1}{x}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{2}}$$

Steps Using Definition of a Derivative

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{0}\times \left(2x\right)^{0}}{x})$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(2x\right)^{0}}{x^{1}})$$

Calculate 2x to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x^{1}})$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})$$

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

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

Subtract 1 from -1.

$$-x^{-2}$$