Solve (2x^-3y/3x^2y^-3)

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

Evaluate

$$\frac{2y^{4}}{3x^{5}}$$

Solution Steps

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

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

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

$$\frac{2y^{4}}{3x^{5}}$$

Differentiate w.r.t. x

$$-\frac{10y^{4}}{3x^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2yy^{3}}{3}x^{-3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{4}}{3}x^{-5})$$

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}.

$$-5\times \frac{2y^{4}}{3}x^{-5-1}$$

Do the arithmetic.

$$\left(-\frac{10y^{4}}{3}\right)x^{-6}$$