Solve 12x^2y^-4/2x^3y^2

$$\frac { 12 x ^ { 2 } y ^ { - 4 } } { 2 x ^ { 3 } y ^ { 2 } }$$

Evaluate

$$\frac{6}{xy^{6}}$$

Solution Steps

Cancel out 2x^{2} in both numerator and denominator.

$$\frac{6y^{-4}}{xy^{2}}$$

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

$$\frac{6}{xy^{6}}$$

Differentiate w.r.t. x

$$-\frac{6}{x^{2}y^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{y^{4}\times 2y^{2}}x^{2-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{y^{6}}\times \frac{1}{x})$$

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}.

$$-\frac{6}{y^{6}}x^{-1-1}$$

Do the arithmetic.

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