Solve -frac{x^{2}y^0}{2yx^-1*(2x^2)^-1}

$$- \frac { x ^ { 2 } y ^ { 0 } } { 2 y x ^ { - 1 } \cdot ( 2 x ^ { 2 } ) ^ { - 1 } }$$

Evaluate

$$-\frac{x^{5}}{y}$$

Solution Steps

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

$$-\frac{y^{0}x^{3}}{2\times \frac{1}{2x^{2}}y}$$

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

$$-\frac{x^{3}}{2\times \frac{1}{2x^{2}}y^{1}}$$

Calculate y to the power of 1 and get y.

$$-\frac{x^{3}}{2\times \frac{1}{2x^{2}}y}$$

Express 2\times \frac{1}{2x^{2}} as a single fraction.

$$-\frac{x^{3}}{\frac{2}{2x^{2}}y}$$

Express \frac{2}{2x^{2}}y as a single fraction.

$$-\frac{x^{3}}{\frac{2y}{2x^{2}}}$$

Cancel out 2 in both numerator and denominator.

$$-\frac{x^{3}}{\frac{y}{x^{2}}}$$

Divide x^{3} by \frac{y}{x^{2}} by multiplying x^{3} by the reciprocal of \frac{y}{x^{2}}.

$$-\frac{x^{3}x^{2}}{y}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-\frac{x^{5}}{y}$$

Differentiate w.r.t. x

$$-\frac{5x^{4}}{y}$$