Solve -10x^8y^13/2x^5y^10

$$\frac { - 10 x ^ { 8 } y ^ { 13 } } { 2 x ^ { 5 } y ^ { 10 } }$$

Evaluate

$$-5\left(xy\right)^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-10\right)^{1}x^{8}y^{13}}{2^{1}x^{5}y^{10}}$$

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

$$\frac{\left(-10\right)^{1}}{2^{1}}x^{8-5}y^{13-10}$$

Subtract 5 from 8.

$$\frac{\left(-10\right)^{1}}{2^{1}}x^{3}y^{13-10}$$

Subtract 10 from 13.

$$\frac{\left(-10\right)^{1}}{2^{1}}x^{3}y^{3}$$

Divide -10 by 2.

$$-5x^{3}y^{3}$$

Differentiate w.r.t. x

$$-15x^{2}y^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{10y^{13}}{2y^{10}}\right)x^{8-5})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$\left(-15y^{3}\right)x^{2}$$