Solve 27x^-6y^-3/3x^-4y^2

$$\frac { 27 x ^ { - 6 } y ^ { - 3 } } { 3 x ^ { - 4 } y ^ { 2 } }$$

Evaluate

$$\frac{9}{x^{2}y^{5}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{9x^{-6}y^{-3}}{x^{-4}y^{2}}$$

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

$$\frac{9}{x^{2}y^{5}}$$

Differentiate w.r.t. x

$$-\frac{18}{x^{3}y^{5}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{27}{y^{3}\times 3y^{2}}x^{-6-\left(-4\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{y^{5}}x^{-2})$$

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}.

$$-2\times \frac{9}{y^{5}}x^{-2-1}$$

Do the arithmetic.

$$\left(-\frac{18}{y^{5}}\right)x^{-3}$$