Solve 24x^-3y^2/-6x^2y^3

$$\frac { 24 x ^ { - 3 } y ^ { 2 } } { - 6 x ^ { 2 } y ^ { 3 } }$$

Evaluate

$$-\frac{4}{yx^{5}}$$

Solution Steps

Cancel out 6y^{2} in both numerator and denominator.

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

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

$$\frac{4}{-yx^{5}}$$

Differentiate w.r.t. x

$$\frac{20}{yx^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24y^{2}}{-6y^{3}}x^{-3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{4}{y}\right)x^{-5})$$

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}.

$$-5\left(-\frac{4}{y}\right)x^{-5-1}$$

Do the arithmetic.

$$\frac{20}{y}x^{-6}$$