Solve 3x^-4y^-3/9x^-2y^1

$$\frac { 3 x ^ { - 4 } y ^ { - 3 } } { 9 x ^ { - 2 } y ^ { 1 } }$$

Evaluate

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

Solution Steps

Cancel out 3 in both numerator and denominator.

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

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

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{y^{3}\times 9y^{1}}x^{-4-\left(-2\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3y^{4}}x^{-2})$$

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}.

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

Do the arithmetic.

$$\left(-\frac{2}{3y^{4}}\right)x^{-3}$$