Solve 12x^3y^-2/18x^-1y

$$\frac { 12 x ^ { 3 } y ^ { - 2 } } { 18 x ^ { - 1 } y }$$

Evaluate

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

Solution Steps

Cancel out 6 in both numerator and denominator.

$$\frac{2y^{-2}x^{3}}{3\times \frac{1}{x}y}$$

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

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

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

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

Differentiate w.r.t. x

$$\frac{8\times \left(\frac{x}{y}\right)^{3}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{y^{2}\times 18y}x^{3-\left(-1\right)})$$

Do the arithmetic.

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

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}.

$$4\times \frac{2}{3y^{3}}x^{4-1}$$

Do the arithmetic.

$$\frac{8}{3y^{3}}x^{3}$$