Solve (x^6y/xy)^-frac{3{2}}

$$( \frac { x ^ { 6 } y } { x y } ) ^ { - \frac { 3 } { 2 } }$$

Differentiate w.r.t. x

$$-\frac{15}{2x^{\frac{17}{2}}}$$

Steps Using Definition of a Derivative

Cancel out xy in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{5}\right)^{-\frac{3}{2}})$$

To raise a power to another power, multiply the exponents. Multiply 5 and -\frac{3}{2} to get -\frac{15}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-\frac{15}{2}})$$

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

$$-\frac{15}{2}x^{-\frac{15}{2}-1}$$

Subtract 1 from -\frac{15}{2}.

$$-\frac{15}{2}x^{-\frac{17}{2}}$$

Evaluate

$$\frac{1}{x^{\frac{15}{2}}}$$