Solve -2x^2y^8/8x^3y^5=

$$\frac { - 2 x ^ { 2 } y ^ { 8 } } { 8 x ^ { 3 } y ^ { 5 } } =$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-2\right)^{1}x^{2}y^{8}}{8^{1}x^{3}y^{5}}$$

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

$$\frac{\left(-2\right)^{1}}{8^{1}}x^{2-3}y^{8-5}$$

Subtract 3 from 2.

$$\frac{\left(-2\right)^{1}}{8^{1}}\times \frac{1}{x}y^{8-5}$$

Subtract 5 from 8.

$$\frac{\left(-2\right)^{1}}{8^{1}}\times \frac{1}{x}y^{3}$$

Reduce the fraction \frac{-2}{8} to lowest terms by extracting and canceling out 2.

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{2y^{8}}{8y^{5}}\right)x^{2-3})$$

Do the arithmetic.

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

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}.

$$-\left(-\frac{y^{3}}{4}\right)x^{-1-1}$$

Do the arithmetic.

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