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

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

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 0 to get 1.

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

Cancel out x^{1} in both numerator and denominator.

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

Calculate x to the power of 0 and get 1.

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

Multiply 2 and -1 to get -2.

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

Expand \left(2x\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

$$-\frac{-2}{4x^{2}}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{3}}$$