Solve frac{4x^-3*y^frac{1{2}}}{6sqrt{x}*y^2}

$$\frac { 4 x ^ { - 3 } \times y ^ { \frac { 1 } { 2 } } } { 6 \sqrt { x } \times y ^ { 2 } }$$

Evaluate

$$\frac{2}{3y^{\frac{3}{2}}x^{\frac{7}{2}}}$$

Short Solution Steps

Cancel out 2\sqrt{y} in both numerator and denominator.

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

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

$$\frac{2}{3y^{\frac{3}{2}}x^{\frac{7}{2}}}$$

Differentiate w.r.t. x

$$-\frac{7}{3y^{\frac{3}{2}}x^{\frac{9}{2}}}$$