Solve (-2x^{3/2}y^-2)(1/2x^-1/4y^5/2z^0)

$$( - 2 x ^ { 3 / 2 } y ^ { - 2 } ) ( \frac { 1 } { 2 } x ^ { - 1 / 4 } y ^ { 5 / 2 } z ^ { 0 } )$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and -\frac{1}{4} to get \frac{5}{4}.

$$-2x^{\frac{5}{4}}y^{-2}\times \frac{1}{2}y^{\frac{5}{2}}z^{0}$$

To multiply powers of the same base, add their exponents. Add -2 and \frac{5}{2} to get \frac{1}{2}.

$$-2x^{\frac{5}{4}}y^{\frac{1}{2}}\times \frac{1}{2}z^{0}$$

Multiply -2 and \frac{1}{2} to get -1.

$$-x^{\frac{5}{4}}y^{\frac{1}{2}}z^{0}$$

Calculate z to the power of 0 and get 1.

$$-x^{\frac{5}{4}}y^{\frac{1}{2}}$$

Differentiate w.r.t. x

$$-\frac{5\sqrt[4]{x}\sqrt{y}}{4}$$