Solve (2xy/-4x^2y^-2)

$$( \frac { 2 x y } { - 4 x ^ { 2 } y ^ { - 2 } } )$$

Evaluate

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

Solution Steps

Cancel out 2x in both numerator and denominator.

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

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

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y}{-\frac{4}{y^{2}}}x^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{y^{3}}{2}\right)\times \frac{1}{x})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-\left(-\frac{y^{3}}{2}\right)x^{-1-1}$$

Do the arithmetic.

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