Solve 2x^-3y^-2/2xy^-5

$$\frac { 2 x ^ { - 3 } y ^ { - 2 } } { 2 x y ^ { - 5 } }$$

Evaluate

$$\frac{y^{3}}{x^{4}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{x^{-3}y^{-2}}{y^{-5}x}$$

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

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

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

$$\frac{y^{3}}{x^{4}}$$

Differentiate w.r.t. x

$$-\frac{4y^{3}}{x^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{y^{2}\times \frac{2}{y^{5}}}x^{-3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y^{3}x^{-4})$$

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}.

$$-4y^{3}x^{-4-1}$$

Do the arithmetic.

$$\left(-4y^{3}\right)x^{-5}$$