Solve 15x^6y^5:(2x^2y^3)=

$$15 x ^ { 6 } y ^ { 5 } : ( 2 x ^ { 2 } y ^ { 3 } ) =$$

Evaluate

$$\frac{15y^{2}x^{4}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}x^{6}y^{5}}{2^{1}x^{2}y^{3}}$$

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

$$\frac{15^{1}}{2^{1}}x^{6-2}y^{5-3}$$

Subtract 2 from 6.

$$\frac{15^{1}}{2^{1}}x^{4}y^{5-3}$$

Subtract 3 from 5.

$$\frac{15^{1}}{2^{1}}x^{4}y^{2}$$

Divide 15 by 2.

$$\frac{15}{2}x^{4}y^{2}$$

Differentiate w.r.t. x

$$30y^{2}x^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15y^{5}}{2y^{3}}x^{6-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15y^{2}}{2}x^{4})$$

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}.

$$4\times \frac{15y^{2}}{2}x^{4-1}$$

Do the arithmetic.

$$30y^{2}x^{3}$$